IGL-Bench: Establishing the Comprehensive Benchmark for Imbalanced Graph Learning
Authors: Jiawen Qin
Haonan Yuan
Qingyun Sun
Lyujin Xu
Jiaqi Yuan
Pengfeng Huang
Zhaonan Wang
Xingcheng Fu
Hao Peng
Jianxin Li
Philip S. Yu
Venue: ICLR 2025 Spotlight (2025)
Keywords: imbalanced graph learning
graph class-imbalance
graph topology-imbalance
comprehensive benchmark
Primary area: datasets and benchmarks
TL;DR: We establish the IGL-Bench, a foundational comprehensive benchmark for imbalanced graph learning, embarking on 17 diverse graph datasets and 24 distinct IGL algorithms with uniform data processing and splitting strategies.

Abstract: Deep graph learning has gained grand popularity over the past years due to its versatility and success in representing graph data across a wide range of domains. However, the pervasive issue of imbalanced graph data distributions, where certain parts exhibit disproportionally abundant data while others remain sparse, undermines the efficacy of conventional graph learning algorithms, leading to biased outcomes. To address this challenge, Imbalanced Graph Learning (IGL) has garnered substantial attention, enabling more balanced data distributions and better task performance. Despite the proliferation of IGL algorithms, the absence of consistent experimental protocols and fair performance comparisons pose a significant barrier to comprehending advancements in this field. To bridge this gap, we introduce **IGL-Bench**, a foundational comprehensive benchmark for imbalanced graph learning, embarking on **17** diverse graph datasets and **24** distinct IGL algorithms with uniform data processing and splitting strategies. Specifically, IGL-Bench systematically investigates state-of-the-art IGL algorithms in terms of **effectiveness**, **robustness**, and **efficiency** on node-level and graph-level tasks, with the scope of class-imbalance and topology-imbalance. Extensive experiments demonstrate the potential benefits of IGL algorithms on various imbalanced conditions, offering insights and opportunities in the IGL field. Further, we have developed an open-sourced and unified package to facilitate reproducible evaluation and inspire further innovative research, available at: https://github.com/RingBDStack/IGL-Bench.

Published as a conference paper at ICLR 2025
IGL-BENCH: ESTABLISHING THE COMPREHENSIVE BENCHMARK FOR IMBALANCED GRAPH LEARNING
Jiawen Qin': Haonan Yuan': Qingyun Sun'; Lyujin Xu', Jiaqi Yuan', Pengfeng Huang',
Zhaonan Wang', Xingcheng Fu", Hao Peng', Jianxin Li Philip S. Yu l Beihang Univerisity GGanggx Normal University University of Illinois, Chicago
(qinjw, yuanhn, sungy, 1ijx @buaa. edu.cn
ABSTRACT
Deep graph learning has gained grand popularity over the past years due to its versa- tility and success representing graph data across a wide range of domains. How- ever, the pervasive issue of imbalanced graph data distributions, where certain parts exhibit disproportionally abundant data while others remain sparse, undermines the efficacy of conventional graph learning algorithms, leading to biased outcomes. To address this challenge, Imbalanced Graph Learning (IGL) has garnered substantial attention, enabling more balanced data distributions and better task performance. Despite the proliferation of IGL algorithms, the absence of consistent experimental protocols and fair performance comparisons pose significant barrier compre- hending advancements in this field. To bridge this gap. we introduce TGI-Rench, foundational comprehensive benchmark for imbalanced graph learning, embark- ing on 17 diverse graph datasets and 24 distinct IGL algorithms with uniform data processing and splitting strategies. Specifically, (GL-Bench, systematically inves- tigates state-of of-the-ar art IGL algorithms in terms of effectiveness, robustness, and efficiency on node-level and graph-leve tasks, with the scope of class-imbalanc and
Extensive experiments demonstrate the potential benefits of IGL. algorithms on various imbalanced conditions, offering insights and opportu- nities in the IGI. field. Further, we have developed an open- open-sourced and unified package to facilitate reproducible evaluation and inspire further innovative research, available at: https: /ttp//gttt/a// com Btt///innnnnngtDaeeeeeeeeee ack IGL -Bench.
INTRODUCTION
Graphs are widely acknowledged as powerful for representing networks such as social networks (Fan et al., 2019), citation networks (Sun et al., 2021; Li et al., 2023a; Sun et al., 2022a), e-commerce networks (Li et al., 2020; Yuan et al., 2023), etc. In graphs, nodes represent individual entities, and edges signify relationships between nodes. Graph representation learning seeks to embed the graph (nodes, edges, or entire graphs) into a low-dimensional space while retaining their structural semantics (Zhang al., 2020). Graph Neural Networks (GNNs) (Kipf & Welling, 2016; Hamilton et al., 2017; Velickovic et al., 2018) have emerged as the dominant approach for graph representation learning owing to their exceptional ability leverage both the graph topology and node properties.
Though GNNs achieve satisfying performance in various tasks, they are typically designed assuming that training data is comprehensive and balanced. However, real-world graph data often feature imbalanced distributions with some parts possessing abundant data while others are scarce (Qin al., 2024), which greatly compromises task performance. The non-Euclidean nature of graph data precludes the use of traditional imbalance learning algorithms, presenting a considerable obstacle to the deployment of GNNs in real-world scenarios. which is also a heated research topic in the community. As graph learning enters the new era of large models, there are number of graph foundation models (Liu et al., 2023a) that depend on a wide range of graph data for pre-training, enabling them to obtain base models that generalize across diverse domains and tasks. Unexpectedly, massive imbalanced graph data inevitably introduces intrinsic biases, presenting significant challenges for subsequent praspt fine-tuning for downstream applications.
"quual contribution. Corresponding author.

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Published as a conference paper at ICLR 2025
Node-Lovel Topology- Imbulance
DEMO Net
tallZvee
Tui--NN ReNode [7]
RaviSGNN [19]
Cold Boew
PASTEL [52]
GraphPtsccter
HepertMBA [12]
Homsopilly
2 Node Level Datasets
Heterophily
Both T Nodes Closs- Imbalance
LTEAG
TAM [89]
CheSeer [65]
Clunclon
Sepimel [44]
TOROAUC
PubMel [65]
Actor [39]
Computers
(48)
ImCAGN GaphSMMTE GraghMixup (50)
GraphliN [37]
CoapaSHA [24]
Photo [46]
oghn-arXGv [14]
VGL-Bende
2019
2020
2021
2022
2023, 2024
GrupheLeed Dutsesss PIC [:]
Graph-Level Juas--Imbllance
GPONN [88]
DanDDee [48]
Imčskis [2-]]
FRANKENSTEIN (16)
PROTEINS
Topalibh [71]
[S]
f
REDDEI-B (64)
Gruph-Leeel Topulogy-Innn Imbolance
SOLF-GNN [32]
ogtp mehhle [14]
COLLAII [22]
Evaluations
Effectiveness (=RQ11, RQ33
Robustness (t- RQ2)
Efficiency (oRQ4)
Figure I: Overview of the established (GL-Bench, Both IGL algorithms and datasets are catego- rized into node-level and graph-level, where the algorithms are further divided into appoloyy-imbllane or both. Click [> and link to the corresponding sections for in-depth analysis.
Imbalanced Graph Learning (IGL.. To address the challenge of imbalance, a wide range of methods have been proposed in the realms of computer vision (Huang et al., 2016) and language (Li et al., 2019) on the broadly concerning class-imbalance learning issue (Johnson & Khoshgoftaar, 2019). Nevertheless, the non-Euclidean graph data presents distinct challenges due its inherent non-i..d. and diverse topological nature. As a result, not only do these conventional methods become infeasible for graphs, but they also fail to address other distinctive topology- imbalance challenges intrinsic in graph data (Zhao et al., 2021; Liu et al., 2021; Chen et al., 2021: Li et al., 2024; 2025). To mitigate the aforementioned imbalanced issues. Imbalanced Graph Learning (IGL) has recently attracted considerable research interest, as highlighted in Figure 1. The increasing literature each year reflects the rising significance and profound effect of tackling IGL challenges, which are categorized into various kinds of research problems, presenting distinct characteristics, necessitating the creation of specialized techniques to handle the imbalance issues inherent to each scenario effectively.
copology-imbllance
Despite the emerging studies of IGL algorithms, there lacks a comprehensive and unified bench- mark, which would significantly impede the understanding and progress of IGL for the following aspects. O Dataset preparation rule. The use of different datasets, data processing approaches, and imbalanced data-splitting strategies in previous works makes many of the results incomparable. @ Experiment conduction protocol. The variability in experimental setups. including parameter settings, initialization procedures, and convergence criteria, hinders reproducibility and comparability across studies. ① Performance evaluation standard. The metrie for evaluating task performance is not consistent. Apart from effectiveness, understanding the efficiency and complexity of each algorithm is imperative, yet often overlooked in the literature. Hence, there is an urgent necessity within the community for the creation of a comprehensive and open-sourced benchmark for IGL.
In this work, we establish comprehensive Imbalanced Graph Learning Benchmark (TGI,Bench)) which serves as the first open-sourced and unified benchmark for graph-specific imbalanced learning to the best of our knowledge. Through benchmarking existing IGL algorithms for effectivvness, robustness, and efficiency, we make the following contributions:
First Comprehensive IGL Benchmark. IGL-Bench enables a fair and unified comparison among 19 ofate-of-the-aan art node-level and 5 graph-level IGL algorithms by unifying the experi- mental settings across 17 graph datasets of diverse characteristics, providing a comprehensive understanding of the class-imbalance and topology-imbalance problems in IGL for the first time.
Multi-faceted Evaluation and Analysis. We conduct systematic analysis of IGL methods from various dimensions, including effectiveness, efficiency, and complexity. Based on the results of extensive experiments, uncover both the potential advantages and limitations of current IGL algorithms, providing valuable insights to guide future research endeavors.
Open-sourced Package. To facilitate future IGL research, we develop an open-sourced bench- mark package for public access. Users can evaluate their algorithms or datasets with less effort.
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Node- Grrahh-Levl Clas--Iballance
Node-Level Topoloy-Imbaalnce
Graph-Level
Topology-Imbalance
Global
4(e)
RC: Under Reaching
graphs Rg graphs
Node
Closs B
d(e)
majority minoerit (C:)
majority (C.)
d(e)
Graph
Class 883
minority (C))
SC: Over-Sgaashing
head nodes
tall nodes T
labeled
unlabeled
max 1-1 Kel
P7. Σ d(u). H.
RC Equation B.4
Gale G.
E H₂
SC + Equation B.5
minj- [y]
T Σ d(v),eeE Tn
1yl.9 E T
10 log |RC SC
M
Figure 2: The research scope of the proposed IGL Bench. Definitions of the imbalance ratio (p)
corresponding to each imbalance issue are further concluded in Table 1. Click and check details.
2 PRELIMINARY AND PROBLEM FORMULATION
Notations. Let G (V be a graph, where V is the node set with N nodes, is the edge set, A RNN is the adjacency matrix, X RRNN Nxd is the node feature matrix with d-dimension.
Node-level Classification. Given the labeled node set V and their labels Yz E RC, where each node 02 is associated with label yı. Semi-supervised node classification aims to train node classifier fo + C to predict the labels Yu of the remaining nodes Vu = V Vz.
Graph-level Classification. Denote G the graph set. Given the labeled graph set G, and their labels Yr E IRC where each graph Gj is associated with a label y.. Graph classification task aims to train graph classifier Fo + RC to predict the labels Yu of the unlabeled graphs G G Gr..
We formulate the IGL. problems into two categories: class-imbalance and nopoloyy-imhalanee where the detailed categorizing motivations and problem descriptions can be found in Appendix B.1.
Definition 1 (Class-Imbalanee Imbalance). There exists an imbalance in the number of labeled samples (nodes or graphs) across different classes, leading to the long-tailed quantity distribution (Ma et al., 2023).
Definition 2 For node-level tasks, an imbalance exists in the topological distribution of labeled nodes, which is brought by two main aspects: 1 Local. Imbalanced node degree distribution (Wu et al., 2019). @ Global. Imbalanced graph structures concerning the Under-reaching and Over-squashing phe- nomenon (Sun et al., 2022b). For graph-level tasks, the imbalance is facilitated by the uneven graph size (the number of nodes) distribution (Liu et al., 2022), which offers potentially biased structures.
Both node- and graph-level tasks encounter topology- imbalance.
aopology-imbalance.
IGL-BENCH: IMBALANCED GRAPH LEARNING BENCHMARK
In this section, we introduce the overview of the IGL-Bench with considerations of the datasets (Section 3.1), algorithms (Section 3.2), and the research questions that guide the benchmark study (Section 3.3). We provide additional details including further declarations in the Appendix.
3.1 BENCHMARK DATASETS
To comprehensively and effectively evaluate the performance of IGL. algorithms, we have integrated 17 real-world datasets from various domains for both the node-level and graph-level tasks. We briefly introduce each category in the following sections. More details are provided in Appendix A.
Node-level Classification Datasets. We utilize 9 graph datasets covering different data scales and homophily, including three citation networks from Plantoid (Yang et al., 2016) (Cora, CiteSeer, PubMed), two co-occurrence networks in Amazon (Shchur et al., 2018) (Computers, Photo), the large-scale orbn-arXiv (Hu et al., 2020), two page-page networks in Wikipedia (Rozemberezki et al., 202.) (Chameleon, Squirrel), and an actor-only induced subgraph of the film- sirrecto--acto-woee network Actor (Pei et al., 2019). Datasets range from strong homophily strong heterophily.
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Table 1: Definitions of the imbalance ratio (p) across different imbalance types.
Imbalance Type
Definition
Explanation
Node-Level Class-Imbalance
max |G
The imbalance ratio is set to the ratio hetween the number of samples ((CT) in the majority and the minority class.
Graph-Level Clas--mbbllanee
min C [cg
H.1 Ed(v).v e Ha
The local imbalance ratio is set to the ratio of the average node degree (d(e)) of the head node set (H,) to the aver- age node degrce of the tail node set (Ta).
Node-Level
17. Ed(o),oe To
hopology-Imbalance
The global imbalance ratio is set to the negative logarithm of the absolute value of the product of the Reaching Coefficient (RC) and the Squashing Coefficient (SC).
(local and global)
P 10 10-1og log| -RC
Graph-Level
Hg Σ Gi E Hl
The imbalance ratio is set to the ratio of the average graph size (number of nodes) of the head graph set (Hg) to the average graph size of the tail gruph set (7p).
Topology-Imbalance
7 9, e T
Graph-level Classification Datasets. We integrate 8 widely adopted real-world datasets. PTC- MR (Bai et al., 2019) and FRANKENSTEIN (Orsini et al., 2015) are molecule datasets, where each graph is a molecule with or without mutagenicity. PROTEINS (Dobson & Doig, 2003; Borgwardt et al., 2005) and D&D (Dobson & Doig, 2003; Shervashidze et al., 2011) are protein datasets marked as enzyme or non-enzyme. IMDB-B (Cai & Wang, 2018) and REDDIT-B (Yanardag & Vishwanathan, 2015) are social networks in movies and online discussions, respectively. The large-scale ogb- molhiv (Hu et al., 2020) is benchmark dataset for predicting the biological activity of molecules, featuring various molecular structures represented as graphs along with corresponding labels. The scientific collaboration dataset COLLAB (Leskovec et al., 2005) for multi-class classification is derived from three publicly available collaboration datasets that represent distinct research fields.
3.2 BENCHMARK ALGORITTMM
Table A.3 conclude the overall 24 IGL algorithms integrated in IGL-Bench with their technique categorization, complexity analysis, and links to implementations (Details in Appendix A.2).
Class-Imbalanced IGL Algorithms. Node-level iinallaebeed IGL refers to the uneven allo- cation of labeled nodes among classes. The classifier prioritizes learning from classes abundant in labeled instances, potentially neglecting those with fewer instances. We implement 10 representative algorithms including DRGCN (Shi et al., 2020), DPGNN (Wang et al., 2021), ImGAGN (Qu et al., 2021), GraphSMOTE (Zhao et al., 2021). GraphENS (Park et al.. 2021), GraphMixup (Wu et al., 2022), LTE4G (Yun al., 2022), TAM (Song et al., 2022), TOPOAUC (Chen al., 2022) and GraphSHA (Li et al., 2023b). Graph-level class-imbalanced IGL. manifests in practical situations where the distribution of labeled graphs across classes is skewed, typically favoring the majority class with more labeled graphs. We select 4 typical algorithms including GºGNN (Wang et al., 2022), Topolmb (Zhao et al., 2022), DataDec (Zhang et al., 2023), and ImGKB (Tang & Liang, 2023).
Topalees-Imbalaneed IGL Algorithms. Node-level -mmallag-i IGL. occurs when the node topology properties display an unequal distribution. An important metric is the node degree, which can reflect the proximity richness. We incorporate DEMO-NE Net (Wu et al., 2019), meta-tail2vee (Liu et al., al., 2020), Tail-GNN (Liu et al., 2021), Cold Brew (Zheng et al., 2021), LTE4G (Yun et al., 2022), RawlsGCN (Kang et al., 2022), and GraphPatcher (Ju et al., 2024a). Another profound topology imbalance is brought by the reaching and over-squashing problem (Sun et al., 2022b), which critically influences the label propagation process. We take ReNode (Chen al., 2021). TAM (Song et al., 2022), PASTEL (Sun et al., 2022b), TOPOAUC (Chen et al., 2022), and HyperIMBA (Fu et al., 2023) as our investigation scope. Graph-level appolog-iimbllnnee IGL stems from the intricate interconnections within graphs. This imbalance frequently presents as variations in graph sizes and topology groups We implement SOLT-GNN (Liu al., 2022) and Topolmb (Zhao et al., 2022).
3.3 RESEARCH QUESTIONS
We systematically design the IGL- Bench to comprehensively evaluate the existing IGL algorithms and inspire future research. In particular, we aim to investigate the following research questions.
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RQ1: How much progress has been made by the existing IGL algorithms?
Motivation and Experiment Design. Existing IGL algorithms are conducted under inconsistent imbalance settings, making it unfair to compare the task performance. Given the fair data and experi- ment environment by IGL-Bench, RQ1 aims to gain a deeper understanding of the strengths and weaknesses of IGL algorithms and identify directions that offer avenues for prospective improvements. To achieve this, we conduct node and graph classifications, where the train/val/test split satisfies the consistent ratio of 1:1:8. We facilitate dataset imbalance with the imbalance ratio p follows definitions in Tabel 1, providing a fair comparison under the same imbalance degree. To perform an unbiased evaluation, we summarize all the metries used in the original papers of the algorithms (Table C.I) and report results with Accuracy (Acc.), Balanced Accuracy (bAcc.), Macro-FI (M-F1), and AUC-ROC. The consensus and focus for each metric are analyzed in Appendix C.2.
RQ2: How effective are the IGL algorithms generalizing to the changing imbalance ratio?
Motivation and Experiment Design. Since RQ1 has already investigated the performance of IGL algorithms on datasets of certain fixed imbalance ratios, RQ2 further explores the robustness of IGL algorithms as the degree imbalance varies by quantitatively controlling the imbalance ratio of each dataset to study the diverse capabilities of IGL. algorithms. To achieve this, we quantitatively set the imbalance ratio to exhibit a staggered distribution of imbalance levels from (relatively) balanced to extremely imbalanced under the predefined splitting constraints.
RQ3: Does classifiers benefit from the IGL algorithms to learn clearer boundaries?
Motivation and Experiment Design. Imbalanced data can cause unexpected shifts of classifier boundary, negatively impacting task performance. RQ3 aims to investigate whether the performance improvement in downstream tasks results from clearer classification boundaries under the influence of the IGL algorithms. To achieve this, we compare changes in inter-class clustering coefficients by the Silhouette score (Rousseeuw, 1987). Additionally, we t-SNE (Van der Maaten & Hinton, 2008) to visualize the learned embeddings, aiding in intuitively understanding boundary shifts.
RQ4: How efficient are these IGL algorithms in terms of time and space?
Motivation and Experiment Design. Existing IGL algorithms handle the imbalance issues generally by redistributing data at either the data level or algorithm level achieve balance, a process that naturally incurs extra computational and spatial complexity compared to vanilla GNNs. However, the algorithm efficiency has been largely overlooked, where RQ4 proposed to understand the trade-off between efficiency and task performance. To achieve this, we evaluate the algorithm efficiency by reporting the training time and peak GPU memory consumption on consistent configurations.
4 EXPERIMENT RESULTS AND ANALYSIS
In this section, compare IGL algorithms covering node-level and graph-level tasks, addressing class-imbalance and topology-imbulance issues. Detailed experiment settings and additional results on more metrics and backbones can be found in Appendix B, Appendix C, and Appendix D.
4.1 EFFECTIVENESS EVALUATIONS FOR IGL ALGORITTMS (RQ1)
4.1.1 EFFECTIVENESS OF NODE-LEVEL CLASS-IMBALANCED ALGORITHMS
Results (Table 2). All algorithms surpass GCN on at least 5 datasets, showing a smaller perfor- mance gain heterophilic graph datasets compared to homophilic ones. @ Compared the resam- pling algorithms (e.g.. ImGAGN, GrapSMOTE, GraphENS, and GraphSHA), data- augtenttgmtttiionn algorithms (e.g., LTE4G and GraphMixup) achieve better performance on 6 out of datasets. O The loss-engineered algorithm TOPOAUC achieves optimal or near-optimal results in 5 out of 7 datasets, attributed its tailored modules for handling iabalaaebba and global @ Over half of the algorithms fail on the large-scale ogbn-ar arxv, while the others perform worse
data,
4.1.2 EFFECTIVENESS OF LEVEL LOCAL TOPOLOGY- -MBLLLNNE ALGORITHMS
Results (Table 3). ① Most algorithms outperform GCN on 7 datasets, with DEMO-Net and Graph- Patcher surpassing GCN on all datasets.
brighhoo-auggmentn algorithms (e.g., Tail-GNN, Cold Brew, and GraphPatcher) achieve greater performance gains compared to model-modified algorithms (e.g., DEMO-Net and RawlsGCN). Tail-GNN and GraphPatcher excel on high-homophily datasets, whereas Cold Brew performs better high- heterhhterophily ones. ! Cases ogbn-arXiv are worse
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Table 2: Accuracy score (% + standard deviation) of node classification on manipulated class- imbalanced graph datasets (Low) over 10 runs. denotes out of memory or time limit. The best results are shown in bold and the runner-ups are underlined (the same for tables below).
Cora
CiteSeer
PubMed
Computers
Photo
ogbn-arXiv
Chameleon Squirrel 0.22
Actor 0.22
Algorithm
0.81
0.74
0.80
0.78
0.82
0.65
0.23
GCN (bb.) [21]
76.36
55.96
60.57a0.19
75 75.06
19.80g1.15
59.8 29.83
26,35go.24
17.16
24.06
DRGON [48]
71.35.0.7
55.22-182
62.59.4.1
67
85.6745.90
26.40+0.35
17.11-081
25.03+0.28
DPONN [57]
72.91
56.78s2.25
81.87
68.69 68.699882
81 11.6629.19
30.58:1.45
25.35-1.48
21.66s1 68
ImGAGI [42]
73.48-1.00
55.29+3.00
12.16
74.92-187
83, 13.144
2..38-286
18.75-1.0
24.54 3..5
GraphSMOTE [70]
77.21=0:27
53.55
71.25a0.27
70.54.1.52
89.07a1.12
27.23
16.79-0.14
25.08an.31
GraphENS [37]
79.34-0.49
61.98+0.66
80.84+0.17
80.72-0.8
90.38-00.7
53. $3.23--0.5
24.34-1.62
20.05-1.61
25.03+0.38
GraphMixup [60]
79.88=0.43
62.6612770
75.9440.09
86.15
56.08
30.95:3.40
17.83-0.32
24.75an.37
LTE4G [67]
80.53a0665
64.48s1.56
83.02.0.33
79.35=1.39
87.94 97.94
31.91=0.44
19.37-0.41
25.43
TAM [49]
80.69e0:27
64. 64.162244
81.47a0.15
81.30
90,35a0.42
53.49.0.54
23.27+1.38
21.17=0.95
24.53
TOPOAUC [8]
83.34
69.03:1.33
70.85
83.72-2.3
33.60=1.51
21.38-1.09
16.0.6
GraphSHA [24]
80.03
60.51
77.9420.6
82.7
91.5550.32
60.30.0.13
23.7321.97
20.05=1.61
23.5921.01
Table 3: Accuracy score (% standard deviation) of node classification on manipulated local dopolog-immbllnnee graph datasets (Mid) over 10 runs. denotes out of memory or time limit.
Cora
CiteSeer
PubMed
Computers
Photo
ogbn-arXiv
Chameleon Squirrel
Actor
Algorithm
0.74
0.65
0.23
0.22
GCN (bb.) [21]
80.16:1.09
66.87
83.97
71.6522.10
89.43
52.93ah.33
52.744000
28.70
21.55
Net [59]
80.37+052
69.73.1.31
84.11
79.38-0.98
38.09+1.0 30
65.81-0.11
55,51+087
39.45.062
29. m2
meta-tuil2vee [30]
32.1740.8
29.97a361
59.8222.86 86
68. 68.17s1.00
79.82+1
33.71
38. 78.044
24.90
26.09.007
Tail-GNN [31]
79.05-1.15
69.97-1.
85.78-0.41
84.09-1.01
92,21-000
53,20+030
30.43+106
28.02-031
Cold Brew [72]
73.84a210
67.42s0.77
86,51s0.4
80. 19.0.4
88. 13:124
69.97
59.162n.40
43.04an24
33.01:019
LTE4G [67]
82.54+0.45
70.55+0.54
84.77+0.7
81.32-22:1
91.09-n.19
55.84+286
32,43+3
44
RawlsGCN [19]
80,52a0.14
86. 42.38.0.4
16.05.0.12
78.7821.40
90.5321.32
40.00
44,962n.79
29.93am65
28.2922224
GraphPatcher [17]
83.25
73.38s0.42 42
35.60
83. 63.688
92.28
66, 74
39.044
36,94
23.85:092
Table 4: Accuracy score (% + standard deviation) of node classification on manipulated global -pgalay-imballeeeed graph datasets (High) over 10 runs.
Algorithm
Cora
CiteSeer
PubMed
Computers
Photo
ogbn-arXiv 0.65
Chameleon 0.23
Squirrel 0.22
Actor
0.81
0.74
0,80
0.78
0.82
0.22
GCN (bb.) [21]
79.10.1.25
68.37a173
83.44an.1
75.02.2.0
86.3221.90
51.04am:18
33.90an.70
23.27=0.:
22.40:0.8
ReNode [7]
79.91=1.52
69.89a77
82.97-0.22
77. 77.95-1.71
87 80-0.2
50.68+0.15
32.92+0:88
23.80-0.90
62.39
TAM [49]
80,50sa11
73.14:013
84.07an11
82.35
89,80.0.23
52.09am0e
35.6420277
24.58s0.9
22.55:006
PASTEL [52]
80.91
72.73a026
83.24:0.85
89. 10.0.1
47.12
33.15-0.66
27.56:1.04
TOPOAUC [8]
79.27-055
70.08-088
75.35-1.32
87. 10-0.0
33.39.2.0
22.86-0.6
36
22.56-0.18
HyperIMBA [12]
79.81
71.78a0.40
84.75an.0
83.43an.6
90.65-0.14
38.30s2.70
29.97a1.2
25.30+2.50
4.1.3 EFFECTIVENESS OF NODE-LEVER GLOBAL
ALGORITTMS
Results (Table 4). Re-weighting IGL algorithms (e.g., ReNode, TAM, and HyperlMBA) generally outperform vanilla GCN on highly homophilic datasets but struggle on heterophilic ones. Structure- refined PASTEL achieves optimal near-optimal results on most datasets, showing significant improvements on highly heterophilic datasets due to its alleviation of both under-reaching and over- squashing phenomena. However, the structure learning mechanism introduces a heavy quadratic computational burden, making PASTEL challenging to adapt to large-scale graphs, e.g., ogbn-arXiv. @ Though algorithms with sub-quadratic complexity (ReNode and TAM) are available on ogbn-arXiv. their performance is greatly weakened due to low-efficiency representation learning and imbalance debias. TOPOAUC has limited ability to address the global topology-imbas -imbalance problem and even performs worse than GCN on heterophilic datasets, which is caused by its homophily assumption.
4.1.4 EFFECTIVENESS OF GRAPH-LEVEI. CLASS- MAAS--MBALLANED ALGORITHMS
Results (Table 5). DataDec achieves optimal or near-optimal results on all datasets. It identifies an informative subset for model training via dynamic sparse graph contrastive learning, which leverages abundant of unlabeled information to enhance the performance. @ G2GNN generally outperforms GIN on binary classification datasets but fails to surpass GIN multi-classification datasets. O Topolmb and ImGKB show considerable instability across different datasets in class- itassiimallanced settings. Despite meticulous hyperparameter tuning detailed in Appendix C to ensure thorough and impartial evaluations, Topolmb cannot be consistently trained to outperform the backbones due to its sensitivity dataset-specific characteristics. O Half algorithms fail on the large-scale ogbg-molhin

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Table 5: Accuracy score (% standard deviation) of graph classification on manipulated class- imbalanced graph datasets (Low) over 10 runs.
Algorithm
PTC-MR FRANKENSTEIN
PROTEINS
D&D
IMDB-B
REDDIT-B
ogbg-molhiv
COLLAB
GIN (bb)) [63]
47.83-2.55
63.38s195
55. 55.38
51.05
62.31
61.10
60.75
65.01
G'GNN [58]
$1.886621
61.13:1.05
63.61
56,29
63.87
69.5843.59
65.00
62.05e306
Topolmh [71]
44.86+1.51
49,4947.4
52.12-10:51
49.9747.4
19.95.5.19
59.6747.00
65.88-0.55
DataDee [68]
55.72=2.88
67.99
66 66.58s1.35
63.51a162
67.92a3.77
78.39:5.01
71.48:1.08
ImGKB [54]
50.1
40.83
66.0022.54
65.85
47.742029
67.50a2.70
48.57
=1.2
Table 6: Accuracy score (% standard deviation) of graph classification on manipulated topology- imbalanced graph datasets (Mid) over 10 runs.
Algorithm
PTC-MR FRANKENSTEIN PROTEINS
D&D
IMDB-B
REDDIT-B
ogbg-molhiv
COLLAB
GIN (bb.) [63]
51.38a6.78
54.82x2.6
62.14:243
61,46-243
65.08
68.3241.77
57.67
65,8423.12
SOLT-GNN [32]
53,04-391
68.71x1.00
71.95:236
63.33-1.56
69.38.1.29
73.51:114
69.69.245
TopoImb [71]
51.59a130
54.52a0.87
64.032443
65.99.1.25
68.10
71.54g075
68.682133
4.1.5 EFFECTIVENESS OF GRAPH-LEVEL TOPOLOGY-IMBLLANCED ALGORITHMS
Results (Table 6). SOLT-GNN surpasses GIN in 5 datasets by transferring head graphs' knowledge to augment tail graphs, showcasing the effectiveness of knowledge transfer mechanisms in improving imbalanced classification. @ Though Topolmb is proposed primarily to address uneven sub-structure distribution, results also demonstrate its ability to alleviate topology-imbalane several datasets. @ Despite recent advancements, significant performance gap persists between current graph-level IGL. algorithms and their node-level counterparts. This observation underscores the need for continued research into more effective strategies to bridge this disparity.
problems across
Key Insights for RQI: Node-level class-imbalance and topology-imbalanee often coexist, posing unique challenges that can be simultancous and orthogonal. For node-level classification, the homophily or heterophily property of the dataset (i.e., the neighbor's label distribution) significantly impacts the learning on llas--ibbllanced and aoology-iibalancee graphs. Currently, there is lack of effective algorithms that address both types of imbalance in large-scale graphs without relying homophily assumptions, underscoring the need for more robust and adaptable solutions.
4.2
ROBUSTNESS TO DIFFERENT IMBALANCE RATIOS (RQ2)
In this section, we quantitatively set the imbalance ratios of each dataset defined in Table I investigate the robustness of IGL algorithms the degree of imbalance varies.
to further
4.2.1 ROBUSTNESS OF NODE-LEVEL CLASS-IMBALAND IMBALANCED ALGORIHTMM
Settings. We manipulate datasets following settings in Appendix B.2 to exhibit staggered imbalance ratio from = 1 to 100 (denoted as Balanced to High). We compare the algorithms' performance changes along with their relative decrease. The single bar chart reflects the algorithm's effectiveness. set of bar charts further illustrates the robustness, and the line chart depicts the algorithm's 's ability to control the performance degradation in an imbalanced data distribution (the flatter, the better).
Results (Figure 3). As the imbalance ratio increases, all node-level IGL algorithms encounter gradual decline in performance. @ Among the class-imbalanced
greater challenges, resulting IGL algorithms, those based on resampling demonstrate better robustness compared to algorithms based on re-weighting and data augmentation. @ For extreme class imbalance (High, = 100), class- ambalance-specife IGL algorithms generally exhibit higher robustness and performance compared to GCN and global topology imbalance methods. Additionally, algorithms designed for both class- and hopoloyy-imbllane (e.g., TAM and TOPOAUC) further enhance performance.
4.2.2 ROBUSTNESS OF NODE- LOCAL TOPOLOGY- IMBALANCE ALGORITTMS
Settings. We manipulate datasets for the node classification following settings in Appendix B.3 with the local -obalagy-imbalance ratios from Low to High. For each dataset, we randomly select training nodes to facilitate different imbalance ratios while ensuring equal number of nodes per class.
Results (Figure 4()). IGL algorithms demonstrate greater robustness in various imbalanced cases, showing more stable performance compared GCN by maintaining consistent performance levels.
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topology imbalance-
100
120
Balanced
Low
High
Relative
Decrcase
Relative Decrease (%)
Accuracy (N)
80-
50
GCN
DROCN
DPGAN
ImGAAN
GophsMOTE
GraphENS
GraphMoup
LTE4G
GlapSSHAA
TAM
TOPOAUC
RoNode
PASTEL
HypetMBBA
20
Figure 3: Robustness analysis of node-level algorithms under different -las-imbeaaace levels on Cora (homophilic). Results are Accuracy and its relative decrease compared to the balanced split.
Compunes
Actor
Chndar
Squin)
Anceoe (80
30.9
22
64
High
High
Cold Brok
GCN Schidd
PASTEL
TAM
GuykENS GayASHA
DEMO-N4
TeLGIN
Crupa
Hlye IMRR
TORoxtiC
(a) Node-level local topology-imie imballaccc
(b) Node-level global copology-imbalane
PIT-MR
PROTFINS
AuaanN (5)
53-
GN
G GNN
Topalmb
DatlDee
lm0KD
GIN SOLF-GNN
Topalmb
(c) Graph-level class-imbalane imbalance.
(d) Graph- topology-inbalanee. imbalance.
Figure 4: Robustness analysis of the node-level and graph-level algorithms under different imbalance levels. Results are reported with the algorithm performance (Accuracy) with the standard deviation.
Different algorithms display varying levels of robustness when facing different types of datasets. and
For example, neighbor-augmente algorithms are robust to extreme local they consistently boost performance the homophilic dataset (e.g., Computers) by a significant margin. Their advantages are even more prominent under higher topology-imbalanee However, they are relatively sensitive to different levels of imbalance in the heterophilic datasets (e.g., Actor).
4.2.3 ROBUSTNESS OF NODE-LEVEL GLOBAL TOPOLOGY- IMBALANCED ALGORITHMS
Settings. We manipulate datasets for the node classification following settings Appendix B.4 with different levels of the global topology-imbalant ratios from Low to High, concerning multiple degrees of the under-reaching and over-squashing phenomena to evaluate algorithm robustness.
Results (Figure 4(b)). All algorithms perform worse in highly imbalanced scenarios due to the difficulty in balancing the uneven topological distributions of training nodes. Topology-imbalanee IGL algorithms generally exhibit robustness across different imbalanced scenarios and tend to enhance performance on both homophilic and heterophilic datasets by utilizing structure learning to alleviate topological imbalance (e.g., PASTEL and HyperlMBA). @ ilaa-eemblenneed GraphSHA synthesizes nodes and connections with different labels, which promotes the global propagation of supervised signals and aids in addressing topological imbalance.
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4.2.4 ROBUSTNESS OF LEVEL
ALGORIHTMM
Settings. Previous research emphasizes the impact of class-imbalance issues on the binary graph classification task. We manipulate datasets for both the binary and multi-class graph classification task following settings in Appendix B.5 with varying levels of daassimmallacee to explore the robustness of IGL. algorithms from Balanced (p = 1) to extremely imbalanced scenarios (High, 100).
Results (Figure 4(c)). I IGL algorithms display varying degrees of robustness on different types of datasets. For example, with an increased imbalance ratio, the performance of IGL gradually decreases on binary classification datasets such as D&D. @ On the contrary, in the multi-class dataset COLLAB, IGL algorithms demonstrate strong robustness across varying levels of imbalance. This indicates that these algorithms can maintain their performance on imbalanced data, effectively handling the complexity and diversity of multiple classes. @ Among these IGL algorithms, DataDec stands out for its remarkable stability in different imbalanced scenarios. consistently shows great performance gains across various datasets, highlighting its effectiveness and reliability.
4.2.5 ROBUSTNESS OF GRAPH LEVEL TOPOLOGY- IMBALNCEE ALGORITTMM
Settings. We manipulate datasets for the graph classification following settings in Appendix B.6 with different levels of the topology-imble imbalance ratios from Low to High, concerning multiple degrees of the graph size distribution to evaluate algorithm robustness.
Results (Figure 4(d)). SOLT-GNN demonstrated remarkable robustness across a spectrum of datasets and topology-imbalane, scenarios, indicating its efficacy in handling varying levels of topology-imbalane @ Contrarily, Topolmb did not consistently surpass GIN and exhibited notable variability in performance across different topology-imbalance degrees, suggesting that Topolmb may not be as reliable in maintaining performance stability for topology-imbalance changes. Ø The results underscore the importance of algorithm choice in graph classification tasks, particularly in scenarios involving
where robustness becomes critical factor.
Key Insights for RQ2: As the imbalance degree increases, the performance tends degrade, especially under extreme conditions. Algorithms tailored to handle either issue demonstrate better robustness in respective contexts. Notably, class-imbalance and topology-imbalanee do not seem to be entirely orthogonal issues. Future research should further investigate the impact of topology and class imbalance on each other in imbalanced graph learning by analyzing their intrinsic causes.
4.3 VISUALIZATIONS THE CLASSIFIER BOUNDARY (RQ3)
Results (Figure 5). Visualizations via SNE Cora and COLLAB illustrate the classifier boundaries, with samples colored by predicted class labels. Quantitatively, the Silhouette score, which ranges from I to 1 (higher values indicate better clustering). provides a clearer view of the clustering of sample embeddings. Results indicate that IGL algorithms effectively reduce class overlap and intuitively shift decision boundaries toward the minority class, enhancing the use of the minor class subspace. This is reflected in higher Silhouette scores for models like G2NNN and DataDec under graph-level class imbalance compared GCN, particularly in challenging conditions.
Key Insights for RQ3: Future research should focus more on exploring dynamic methods to adjust boundary sensitivity in response to imbalanced data, which could further enhance classification performance. Additionally, incorporating attention mechanisms or adversarial training techniques improve boundary clarity under more extreme imbalanced conditions can offer stronger defenses against adversarial attacks and boost generalization to diverse biased graph data.
4.4 EFFICIENCY AND SCALABILITY ANALYSIS (RQ4)
Results (Figure 6). As we can observe, IGL algorithms generally have higher time or space com- plexity compared to backbones. Some algorithms (e.g., GraphMixup, LTEE4 and DataDec) can achieve relatively good performance improvement with less complexity increase, Besides, although some algorithms (e.g. TOPOAUC, GraphPatcher and PASTEL) achieve remarkable effectiveness improvement, they largely increase the complexity of time and space. Additionally, the efficiency problem of IGL is specially pronounced on the large-scals dataset (ogbn-arXiv), shown in Tables 2, 3, and 4, nearly half of IGL algorithms run out of memory. IGL algorithms struggle to achieve a satisfactory balance between performance and efficiency. Additional results in Appendix D.

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Published as a conference paper at ICLR 2025
OCN
TAM
LTB4G
GCN
Cold Brew
CraphPatcher
Silouttic Scoee: 0.26
Siloudic Scre:: 0.36
Sihouatte Sour: 0.35
Sihoudiic Soore: 0.25
Silbouate Scar: 0.12
Silooatte Saure: 0.31
(a) Node-level class-imbllane (Cora, Low).
(b) Node-level local topology-imbalance imbalance (Cora, Mid),
TOMAUC
PASTIZ
Danabee
GONN
Silboratte Scomt: D.51
Silborate Stoee U131
Silbocitee Soore: 0.33
Silhrusttr Scone
Silbeaste S.55:
Silouree Soore 0.55
(c) Node-level global copology-imbalane (Cora, High). (d) Graph-level class-imbalance (COLLAB, Low).
Figure 5: Visualization of node- and graph-level IGL algorithms in varying imbalanced scenarios.
(Low)
PROTEINS (Low)
PROTEINS
Fass
TOROADE
DEMD
11540
TAMM
Dandic a
77
BE4DN
Rolosa
Bur
75
IKK.GG
TUPOALE
HlportMBA
Towbes
76
Tince
Trainiea
Trsining Timee
Tratting Time (1)
83
83
DASTEL
76
11142
TAM
NPVD
TAM
56-
27
Tandvey
Buhaaz
05
190
2000
1000
2000
1900
50
100
150
100
Trainin
Training Space
Squce
Traising Spece (MB)
Traising Space (Topology Imbalance)
(Class- Imbalanne
(Local Topolagy-imballnce) Imbalance)
(Global (opology-Lmballncee)) Imbalance)
(Class Ambalance)
Figure 6: Time and space analysis of node- and graph-level IGL algorithms on Cora and Proteins.
Key Insights for RQ4: Graph learning for ultra-large-scale data is prominent research frontier the community. The new paradigm of graph foundation models poses substantial challenges in memory- -emoor-time--efcciienly addressing imbalanced graph data and achieving high-quality rep- resentation learning. Investigating graph representation frameworks built on models like graph transformers, and state space models, etc., presents promising avenue for future development.
5 CONCLUSION AND FUTURE DIRECTIONS
This paper introduces the first comprehensive imbalanced graph learning benchmark, IGL Bench, by integrating 24 methods across 17 graph datasets. We conduct extensive experiments to reveal the performance of IGL algorithms in terms of effectiveness, robustness and efficiency on node-level and graph-level tasks. We design and implement package ICL-Bench (https: //gi/ thub. com/ wainggDSttak/II...... algorithms, processed datasets, and scripts reproduce the results in this paper. Drawing upon our empirical analysis and insights, we point out some promising future directions for IGL community:
that incorporates all the aforementioned protocols, baseline
O Unified Algorithm. Class-imbalance and appoloy-iibbllnee simultaneously and widely exist in multi-domain graphs. Future research should revisit the optimization conflicts between two imbalance issues and develop a unified "one for both" IGL algorithm rooted in core nature of the problem.
@ Robustness and Generalization. The practicality of IGL algorithms in real-world applications essential. Future research should emphasize enhancing the robustness of IGL algorithms in extreme imbalance scenarios and improving their generalization to handle unseen testing domains or unprecedented distribution shifts, ensuring reliable performance in diverse real-world settings.
0 Efficiency and Scalability, Empirical evidence suggests that current IGL. algorithms struggle, or are infeasible to operate efficiently on large-scale graphs. As the size of graphs continues to grow exponentially, a key area of future research is the reduction of memory and computational complexity IGL algorithms to ensure their efficient scalability and performance on large-scale graphs.
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ACKNOWLEDGMENTS
The corresponding author is Jianxin Li. This research was supported in part by the National Natural Science Foundation China (NSFC) under Grants No. 62225202 and No. 62302023, the Fundamen- tal Research Funds for the Central Universities, and the National Science Foundation (NSF) under Grants III-2007558 and POSE-2346158. We owe sincere thanks all authors for their valuable efforts and contributions.
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Chunhui Zhang, Chao Huang, Yijun Tian, Qianlong Wen, Zhongyu Ouyang, Youhuan Li, Yanfang Ye, and Chuxu Zhang. When sparsity meets contrastive models: Less graph data can bring better class-bake balanced representations. In /CML, pp.
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Tianxiang Zhao, Xiang Zhang, and Suhang Wang. Graphsmote: Imbalanced node classification on graphs with graph neural networks. In WSDDM, pp. 833-841, 2021.
Tianxiang Zhao, Dongsheng Luo, Xiang Zhang, and Suhang Wang. Topoimb: Toward topology-level imbalance in learning from graphs. In LOG, pp. 37-1. PMLR, 2022.
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Appendix
Table of Contents
Datasets and Algorithms
16
A.1 Benchmark Datasets
16
A.2 Benchmark Algorithms
17
B Details of the Dataset Settings
21
B.1 Imbalance Ratio Definition
21
B.2 Manipulated elasa-Imbalanced Datasets for Node Classification
23
Manipulated Local Topology-Imbalanced Imbalanced Datasets Node Classification
25
B.4 Manipulated Global hopology-Imbalanee Datasets for Node Classification
26
B.5 Manipulated Class hasslamebleeeeed Datasets for Graph Classification
27
B.6 Manipulated Topology-Imballnn Imbalanced Datasets for Graph Classification
28
C Details of the Experimental Settings
29
C.I General Experimental Configurations
29
Evaluation Metries
29
C,3 Hyperparameter
31
C.4 Computation Resouces
33
D Additional Experimental Results
33
D.1 Additional Results for Algorithm Effectiveness ................................
33
D.2 Additional Results for Algorithm Robustness (RQ2)
................................
48
D.3 Additional Results for Visualizations (RQ3)
D.4 Additional Results for Efficiency Analysis ................................
52
(...............................
E Package and Reproducibility
56
F Further Discussions
57
F.1 Related Works
57
F2 Limitations
57
F3 Dataset Privacy and Ethics
58
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A DATASETS AND ALGORITTMS
A.1 BENCHMARK DATASETS
We adopt 17 benchmark datasets since 1 they are extensively utilized for training and assessing IGL algorithms: @ they encompass broad range of graph properties, spanning from small-scale to large-scale, from homophilic to heterophilic, and from node-level to graph-level; @ they cover diverse domains including citation networks, social networks, website networks, biochemicals, and co-occurrence networks. All the datasets integrated into our IGL-Bench are either published or publicly accessible. Table A.I and Table A.2 provide the detailed statisties of the benchmark datasets, and their detailed descriptions are as follows.
Cora (Yang al., 2016) a citation network dataset containing scientific publications classified into one of seven research areas, Each publication is represented by a feature vector indicating the presence or absence of words. The task to predict the one-hot category label of given publication. The dataset is licensed under Creative Commons 4.0.
CiteSeer (Yang et al., 2016) is a citation network dataset, consisting of scientific publications, each labeled with one of six classes the ont-hot vector form. commonly used for tasks such document classification and citation prediction. The dataset is licensed under Creative Commons 4.0.
PubMed (Yang et al., 2016) a dataset of the biomedical literature, commonly used for tasks like document classification, information retrieval, and citation analysis. Each document associated with a one-hot MeSH (Medical Subject Headings) topic label, which is used for document classification. The dataset licensed under Creative Commons 4.0.
Computers (Shchur et al., 2018) and Photo (Shchur et al., 2018) are Amazon products co- occurrence networks. Nodes represent goods and edges represent that two goods are frequently bought together. The task is to map goods to their respective product category. The datasets are licensed with MIT License.
ogbn-arXiv (Hu al., 2020) is benchmark citation network derived from the arXiv website, consisting of a large number of nodes and edges, covering wide range of research fields. Each node represents a paper, which described by the word embeddings extracted from the title and abstract. Each directed edge indicates the citations between papers. It is used for tasks such as node classification and link prediction in academic citation networks. The dataset licensed under ODC-BY.
Chameleon (Rozemberezki et al., 2021) and Squirrel (Rozemberezki et al., 2021) are the Wikipedia page-page networks. Nodes represent web pages and edges represent hyperlinks between them. Node features represent several informative nouns the Wikipedia pages. The task is to predict the average daily traffic the web page. The datasets are licensed with GPL-3.0 License.
Actor (Pei et al., 2019) the actor-only induced subgraph of the film-director-actto-vvii network. Each node corresponds to an actor, and the edge denotes co- co-occurrence on the same Wikipedia page. Node features represent keywords on the Wikipedia pages. The task is to classify nodes into five categories from the actor's Wikipedia. The dataset is made public with a license unspecified.
PTC-MR (Bai et al., 2019) is a dataset of chemical compounds labeled with their mutagenic activity bacteria. It has 344 molecules with binary label indicating the carcinogenicity of compounds in rodents. It is used for tasks such as chemical compound classification and toxicity prediction. The dataset is made public with license unspecified.
FRANKENSTEI (Orsini et al., 2015) a set of molecular graphs with node features containing continuous values. A label denotes whether molecule is a mutagen non-mutagen. The dataset is made public with a license unspecified. The dataset licensed under Creative Commons 1.0.
(Borgwardt et al., 2005) is a set macromolecules derived from Dobson and Doig, where nodes structure elements. Edges denote nodes in an amino acid sequence or close 3D space. The task is to predict whether a protein an enzyme. The dataset licensed under Creative Commons 4.0.
PROTEINS
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Table A.I: Statistics of benchmark datasets for node classification.
Dataset
# #Nodes
EEdges
# Claasses
Features
Avg. # Degree
Homophily
Cora [65]
2,708
5,278
7
1,433
3.90
0.81
CiteSeer [65]
3,327
4,614
6
3,703
2.77
0.74
PubMed [65]
19,717
44,325
3
500
4.50
0.80
Computers [46]
13,752
245,861
767
35.76
0.78
Photo [46]
7,487
119,081
8
745
31.13
0.82
ogbn-arXiv [14]
169,343
1,157,799
40
767
13.67
0.65
Chameleon [44]
2,277
36,101
5
2,325
27.60
0.23
Squirrel [44]
5,201
217,073
5
2,089
76.33
0.22
Actor [39]
7,600
26,659
5
932
7.02
0.22
Table A.2: Statistics of benchmark datasets for graph classification.
Avg. Nodes
Avg. # Edges
Avg. Degree
Dataset
#Graphs
# Classes
# Features
heud
PTC-MR [1]
344
14.29
14.69
2
18
2.06
67
FRANKENSTEIN [36]
4,337
16.90
17.88
2
780
2.12
757
PROTEINS [2]
1,113
39.06
72.82
2
3
3,73
218
D&D [47]
1.178
284.32
715.66
2
89
5.03
234
IMDB-B [5]
1,000
19.77
96.53
2
65
9.77
194
REDDIT-B [64]
2,000
429.63
497.75
2.32
400
ogbg-molhiv [14]
41,127
25.51
27.50
2
9
4.29
8,225
COLLAB [22]
5000
74.49
2457.78
3
369
65.99
991
D&D (Shervashidze et al., 2011) contains graphs of protein structures. node represents an amino acid and edges are constructed the distance two nodes less than 6Å. The label denotes whether protein is an enzyme non-enzyme. The dataset is made public with license unspecified.
IMDB-B
(Cai & Wang, 2018) movie collaboration dataset where actor/actress and genre information of different movies are collected. For each graph, nodes represent actors/actresses and there an edge between them they appear the same movie. The dataset licensed under Creative Commons 4.0.
REDDIT-B (Yanardag & Vishwanathan, 2015) is balanced dataset where each graph corre- sponds online discussion thread where nodes correspond users, and there is edge between two nodes if at least one of them responds to another's comment. The dataset is licensed under Creative Commons 4.0.
ogbg-molhiv (Hu et al., 2020) is natural imbalanced molecular dataset, consisting of large number of graphs. Each graph represents a molecule, where nodes are atoms, and edges are chemical bonds. Node features contain atomic number and chirality, well as other additional atom features. The dataset is made public with an MIT License.
COLLAB (Leskovec et al., 2005) is the scientific collaboration dataset, deriving from three public collaboration datasets. The networks of researchers were generated from each field, and each was labeled as the researcher field. The task is to determine to which field the collaboration network of researcher belongs. The dataset is licensed under Creative Commons 4.0.
A.2 BENCHMARK ALGORITTM
In our developed IGL- Bench, we integrate 24 state-of-the-art IGL algorithms. including 10 node- level class- clas-iibbllanced IGL algorithms: DRGCN (Shi et al., 2020), DPGNN (Wang et al., 2021),
We report node homophily ratio that normalizes the edge homophily across neighborhonds (Pei al., 2019). For each dataset, we divide graphs into head and tail with a predefined ratio based on the Pareto princi- ple Sanders (1987) (also known as 20/80 rulc) to employ the 20% largest graphs as head graphs, and the rest. 80% tail graphs.
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Table A.3: Summary of representative Imbalanced Graph Representation Learning (IGI.) algorithms integrated in IGL CCL-Ber Be.-Ben.c concerning the imbalance types, downstream tasks, method levels, and computational complexity. We also provide public access the official algorithm implementations.
Data-Level
Algorithm-Lewe
Computational Complexity
Type
Algorithm
Task
Code
IG AG PL
MR
Loss
RG
DRGCN [48]
NC
O(V) + (g])
link
DPGNN [57]
NC
O(1) + (8)
link
ImGAGN [42]
NC
O(V] + (&)
link
GraphSMOTE [70]
NC
((()))) + O(EE)
link
Node-Level
GraphENS [37]
NC
0(V) + (8)
link
Class-Imbalance
GraphMixup [60]
NC
((V))) + O(E))
link
LTE4G [67]
NC
0(1()) +O(E))
link
TAM [49]
NC
O(VIC+18)
link
TOPOAUC [8]
NC
+8)
link
GraphSHA [24]
NC
O(V) + (8)
link
DEMO-Net [59]
NC
O(V) + (8)
link
meta-tail2vee [30]
NC
SS5
O( + (E)
link
Tail-GNN [31]
NC
O(V)
link
local
Cold Brew [72]
NC
O(1V+ (8)
link
LTE4G [67]
NC
((1V)) +((E))
link
Node-Level
RawlsGCN [19]
NC
((V++
link
Sopology-Imbalance
GraphPatcher [17)
NC
0(V)+18)
link
ReNode [7]
NC
0(V)+
link
TAM [49]
NC
D(VIC+
link
global PASTEL [52]
NC
0(1)+ O(EE)
link
TOPOAUC [8]
NC
+(V)+
link
HyperIMBA [12]
NC
4
0(V++
link
G:GNN [58]
GC
o(1 max 1 (S)
link
Graph-Level
Topolmb [71]
NC, GC
O + g.-
link
Class-Imbalance
DataDec [68]
NC, GC
link
ImGKB [54]
GC
() + ()
link
Graph-Level
SOLT-GNN [32]
GC
O (..1)
link
Sipology-Imbllnne
Tupolmb [71]
NC, GC
O2 ( link
ImGAGN (Qu et al., 2021), GraphSMOTE (Zhao al., 2021), GraphENS (Park et al., 2021),
GraphMixup (Wu et al., 2022), LTE4G (Yun et al., 2022), TAM (Song et al., 2022), TOPOAUC (Chen al., 2022) and GraphSHA (Li al., 2023b); 12 node-level topology-imbalaneed IGL algorithms: DEMO-Net (Wu et al., 2019), meta-tail2vec (Liu et al., 2020), Tail-GNN (Liu et al., 2021), Cold Brew (Zheng et al., 2021), LTE4G (Yun al., 2022). RawlsGCN (Kang al., 2022), GraphPatcher (Ju et al., 2024a), ReNode (Chen et al., 2021). TAM (Song et al., 2022), PASTEL (Sun et al.. 2022b), TOPOAUC (Chen et al., 2022), and HyperlMBA (Fu et al., 2023); graph-level class-imbalanced IGI. algoriths:: GCGNN (Wang et al., 2022), Topolmb (Zhao et al., 2022), DataDec (Zhang et al., 2023), and ImGKB (Tang & Liang, 2023); graph-level topology-imbalane imbalanceee IGL algorithms: SOLT-GNN (Liu et al., 2022) and Topolmb (Zhao et al., 2022).
We conclude the aforementioned representative IGL algorithms in Tabel A.3 in terms of the down- stream task, method level, and computational complexity. The Task column indicates the specific downstream tasks the algorithm can handle, where "NC" stands for node classification, and "GC" stands for graph classification. The Data-Level column implies the algorithm handles the imbalance issue from the training data perspective, where "IG" stands for generating samples by interpolating, "AG" stands for generating samples by adversarial training, and "PL" stands for generating pseudo labels for a large number of unlabeled nodes. The Algorithm-Level column suggests an algorithm- level contribution to solve the imbalance learning problems, where "MR" denotes refining GNN models for improving the representation learning process, "Loss" represents designing or engineering loss function for sample reweighting, etc., and "RG" stands for utilizing extra regularizers for the imbalance recalibrating, We further introduce all the IGL algorithms as follows.
For brevity, only the main bottlenecks of the algorithm's 's computational complexity analyzed here, while the remaining negligible parts are uniformly ignored. The meanings of notations follow definitions in Section 2.
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DRGCN (Shi et al., 2020) is proposed to address the node-level class-imbalance issue. It employs a GNN strategy, incorporating a conditioned generative adversarial network (GAN) create synthetic nodes to balance redistribution. Additionally, it utilizes a KL-divergence constraint to harmonize the representation distribution of unlabeled nodes with that of labeled ones. The code is made available with a license unspecified.
DPGNN (Wang et al., 2021) is proposed to address the node-level class-imbalance issue. employs a class prototype-driven training approach to balance training loss across classes and transfer knowledge from head classes to tail classes, with the help of distance metric learning accurately capture the relative positions of nodes concerning class prototypes, as well as smoothing representations of adjacent nodes while separating interclass prototypes. The code is made available with a license unspecified.
ImGAGN (Qu et al., 2021) is proposed to address the node-level blass-mmbllance issue. It applies the generative adversarial network (GAN) generate synthetic nodes, which simulates both the minority class nodes' attribute distribution and network topological structure distribution by generating a set of synthetic minority nodes such that the number of nodes in different classes can be balanced. The code is made available with license unspecified.
GraphSMOTE (Zhao al., 2021) is proposed address the node-level class- btass-imallance issue. It evolves around the generation of synthetic nodes to balance classes by technique inspired by SMOTE (Chawla et al., 2002), which is the first data interpolation method on graphs by generating a synthetic minority node through interpolation between two real minority nodes in the embedding space. It pre-trains an edge predictor using a graph reconstruction objective on real nodes and existing edges to determine the connectivity between the synthetic node and existing nodes. The code is made available with a license unspecified.
GraphENS (Park et al., 2021) is proposed to address the node-level class-imbalance issue. It creates a synthetic minority node by blending real minority node with a randomly chosen target node. Notably, GraphENS (Park al., 202 1) prioritizes the neighbors of minority nodes, recognizing their significant informational value. To address this bias, it incorporates neighbor sampling and saliency- basee node mixing techniques. The code is made available with an MIT License.
GraphMixup (Wu et al., 2022) is proposed address the node-level iaas-imballane issue. GraphMixup (Wu et al., 2022) executes reinforcement mixup within the semantic space instead of the input or embedding space, thereby averting the creation of out-of-domain minority samples. It integrates two supplementary self-supervised learning objectives: local-path prediction and global-path prediction, aiming to encompass both local and global insights within the graph structure. The code is made available with an MIT License.
LTE4G (Yun et al., 2022) is proposed to address the node-level class-imbalance issue. It takes into account the imbalance in both node classes and degrees. LTE4G (Yun et al., 2022) divides nodes into balanced subsets and assigns them specialized Graph Neural Networks (GNNs) based on their similarity to each class prototype vector. The class with the highest similarity score is assigned each node subset. Subsequently, LTE4G (Yun et al., 2022) utilizes knowledge distillation to train class-specific student models, thereby improving classification performance. The code is made available with a license unspecified.
TAM (Song et al., 2022) is proposed to address the node-level class imsallnce issue and topology- imbalance issue simultaneously. TAM (Song et al., 2022) resolves the glass-imbalance issue by integrating graph topology information into its loss function designs and addressing the de- creased homogeneity among minority nodes. Particularly, TAM (Song et al., 2022) introduces connectivity- and distribution-anu margins to guide the model, highlighting class-wise connec- tivity and neighbor- label distribution in an innovative manner. The code is made available with an MIT License.
TOPOAUC (Chen et al., 2022) is proposed to address the node-level class-imbalance and -inallaane issue simultaneously. It develops a multi-class AUC optimization work to deal with the class imbalance problem. With respect to topology imbalance, TOPOAUC (Chen et al., 2022) proposes a Hopology-Award Importance Learning mechanism (TAIL), which consid- ers the topology of pairwise nodes and different contributions of topology information to pairwise node neighbors. The code is made available with license unspecified.
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GraphSHA (Li at., 2023b) is proposed to address the node-level class-imbalance issue. It aims to expand the decision boundaries of minority classes by generating more challenging synthetic samples from these classes. Additionally, GraphSHA (Li et al., 2023b) introduces module named SemiMixup, which is designed to transfer the enlarged boundary information into the interior of the minority classes while preventing the leakage of information from the minority classes to their neighboring majority classes. This helps to enhance the separability of minority classes without compromising their integrity. The code is made available with an MIT License.
DEMO-Net (Wu et al., 2019) is proposed to address the nodc-level applooyyimballane spired by the Deisfeiler-Lehmall graph isomorphism test, DEMO-Net (Wu et al., 2019) explicitly captures integrated graph topology and node attributes. It introduces multi-task graph convolution, where each task focuses on learning node representations for nodes with specific degree values, thereby preserving the degree-specifie graph structure. Furthermore, DEMO-Net (Wu et al., 2019) devises a new graph-level pooling/readout scheme to learn graph representations, ensuring they reside in degree-specific Hilbert kereel space. The code is made available with license unspecified.
issue. In-
meta-tail2vee (Liu et al., 2020) is proposed to address the node-level local topology-imbel imbalance issue. It frames the objective of learning from imbalanced data, particularly focusing on learning embeddings for tail nodes, as a few-shot regression task, considering the limited connections associated with each tail node. Moreover, meta-tail2vec (Liu et al., 2020) recognizes that each node exists within its unique local context and therefore adapts the regression model individually for each tail node, personalizing the learning process. The code is made available with an MIT License.
Tail-GNN (Liu et al., 2021) is proposed to address the node-level local copology-imbalane issue. While GNNs are capable of learning effective node representations, they often handle all nodes in generic manner and do not specifically cater to the numerous tail nodes. Tail-GNN (Liu et al., 2021) leverages the innovative concept of transferable neighborhood translation to capture the diverse relationships between a node and its neighboring nodes. In essence, Tail-GNN (Liu et al., 2021) develops a node-specific adaptation technique that tailors the global translation to the individual needs of each node. The code is made available with license unspecified.
Cold Brew (Zheng et al., 2021) is proposed to address the node-level local topology-imbalann imbalance issue, with a particular focus on the most extreme cases in graphs where node lacks any
neighboring connections, known as the Striet Cold Start (SCS) problem (Qian et al., 2020). Cold Brew (Zheng al., 2021) employs a teacher-student distillation framework to address the SCS issue and the challenge posed by noisy neighbors in the context of GNNs. Additionally, Cold Brew (Zheng et al., 2021) introduces the concept of feature contribution ratio, a metric that quantifies the performance of inductive GNNs in resolving the SCS problem. The code is made available with an Apache-2.0 License.
RawlsGCN (Kang et al., 2022) is proposed to address the node-level local topology-imbalance issuc. It approaches the issue of degree-related performance disparities through the lens of the Rawlsian difference principle, a concept derived from the theory of distributive justice. RawlsGCN (Kang et al., 2022) is designed to equalize the performance between nodes with low and high degrees while also optimizing for task-specific objectives, ensuring fairer allocation of predictive utility across the graph. The code is made available with an MIT License.
GraphPatcher (Ju al., 2024a) is proposed address the node-level local ropoloyyimballnee issue. It suggests a test-time augmentation framework designed to improve the test-time gener- alization ability of any GNNs for low-degree nodes. In detail, GraphPatcher (Ju al., 2024a) successively creates virtual nodes to repair the artificially generated low-degree nodes through corruptions, with the goal of incrementally reconstructing the target GNN's 's predictions across a series of progressively corrupted nodes. The code is made available with a license unspecified.
ReNode (Chen et al., 2021) is proposed to address the node-level global topology-imbalanee imbalance issue. ReNode (Chen et al., 2021) adjusts the weights of labeled nodes according to their proximity to class boundaries, thereby enhancing performance, especially for nodes near boundaries and those distant from them. Additionally, metric is devised to measure this imbalance, utilizing influence conflict detection. ReNode (Chen et al., 2021) effectively addresses both plass-imbalance and topology-imbalance challenges concurrently. The code is made available with an MIT License.
PASTEL (Sun et al., 2022b) is proposed to address the node-level global topology-imbaland issue PASTEL (Sun et al., 2022b) addresses topology imbalance by optimizing the paths of
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information propagation. Its goal is to mitigate the under-reaching and over werr-squshing effects by improving intra-class connectivity and employing a position encoding mechanism. Additionally, PASTEL (Sun et al., 2022b) utilizes class-wise conflict measure for edge weights to aid in node class separation. The code is made available with an MIT License.
HyperIMBA (Fu et al., 2023) is proposed to address the node-level global topology imbalance issue. HyperIMBA (Fu et al., 2023) employs hyperbolic geometric embedding to assess the then modifies label information propagation and adjusts the
hierarchy of labeled nodes. objective margin according to the node's hierarchy, effectively tackling issues arising from hierarchy imbalance. The code is made available with a license unspecified.
G2GNN (Wang al., 2022) is proposed address the graph-level class-imbalance issue. It employs additional supervision at both global and local levels: globally, through neighboring graphs, and locally, via stochastic augmentations. G2GNN (Wang al., 2022) constructs Graph of Graphs (GoG) by utilizing kernel similarity and implements GoG propagation for information aggregation. Furthermore, utilizes topological augmentation with self- consisteccy regularization at the local level. These combined strategies improve model generalizability and consequently enhance classification performance. The code is made available with license unspecified.
Topolmb (Zhao et al., 2022) is proposed to address the graph-level class-imbalance and topology- imbalance issues. Graph-level topology imbalance often stems from uneven motif distribu- tion (e.g., functional groups), resulting in a lack of training instances for minority groups TopoImb (Zhao et al., 2022) tackles this challenge by dynamically updating the identification of topology groups and assigning importance weights to under-represented instances during training. This approach enhances the learning efficacy of minority topology groups and mitigates overfitting to majority groups. The code is made available with a license unspecified.
DataDec (Zhang et al., 2023) is proposed to address both the node-level and graph-level class- imbalance issues. DataDec (Zhang et al., 2023) develops a unified data-model dynamic sparsity framework to address challenges brought by training upon massive class-imbalanced graph data. The key idea of DataDec (Zhang et al., 2023) is identify the informative subset dynamically during the training process by adopting sparse graph contrastive learning. The code is made available with a license unspecified.
ImGKB (Tang & Liang, 2023) is proposed to address the graph-level class-imbalance issue. It combines the restricted random walk kernel with the global graph information bottleneck (GIB) (Wu et al., 2020) to enhance the performance of imbalanced graph classification tasks. To prevent the dominant class graphs from introducing redundant information into the kernel outputs, ImGKB (Tang& & Liang, 2023) frames the entire kernel learning process Markovian decision process. It then utilizes the global GIB (Wu et al., 2020) approach to optimize the learning, ensuring that the kernel effectively captures the relevant information for each class. The code made available with license unspecified.
SOLT-GNN (Liu et al., 2022) is proposed to address both the graph-level topology-imbalance issues. Graphs with larger sizes (number of nodes) tend to possess more complex topological structures. To counter performance biases caused by the intricate topological structures, SOLT- GNN (Liu et al., 2022) enhances the performance of smaller graphs. It identifies co-occurrence patterns in larger graphs (or "head" graphs) and transfers this knowledge to augment smaller graphs, improving their performance. The code is made available with license unspecified.
B DETAILS OF THE DATASET SETTINGS
B. IMBALANCE RATIO DEFINITION
We provide additional explanations on the details of the imbalance ratio defined in Tabel 1.
Node/Graph-Leve Class-Imbalann Imbalance. Given set of labeled training node/graph classes V2= Uisise C, the imbalance ratio is defined to be the ratio between the number of nodes/graphs in the majority class and the number of nodes/graphs in the minority class, i.e.,
max |c,l
p
(B.1)
min j= [C,l
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Table B.1: Definitions of the imbalance ratio (p) across different imbalance types.
Imbalance Type
Definition
Explanation
Node-Level Class-Imbalance
max |G
The imbalance ratio is set to the ratio hetween the number of samples ((CT) in the majority and the minority class.
Graph-Level Tlasalama
ming C [cg
H.1 Ed(v).v e Ha
The local imbalance ratio is set to the ratio of the average node degree (d(e)) of the head node set (H,)) to the aver- age node degrce of the tail node set (Ta).
Node-Level
17. Ed(o),e To
hopology-Imbalance
The global imbalance ratio is set to the negative logarithm of the absolute value of the product of the Reaching Coefficient (RC) and the Squashing Coefficient (SC).
(local and global)
P 10 10-1og log| (RC-SC)
Graph-Level
Rgj Σ Di E Hl
The imbalance ratio is set to the ratio of the average graph size (number of nodes) of the head graph set (Hg) to the average graph size of the tail graph set (7p).
Topology-Imbalang,
7i 9 e T
Node-level dlas-imbalaance occurs when there is an uneven spread of labeled nodes among different classes. This can lead the model prioritize learning from classes abundant in labeled instances, potentially neglecting those with fewer examples. Graph-level is similar to node-level class-imbalance. This issue frequently arises in practical contexts, such as imbalanced chemical compound classification, where the distributions of labeled graphs are skewed. Typically, this bias favors the majority class, which comprises more labeled graphs.
Node-Level Yopology-Imbalance
Local Imbalance. Given a set of labeled nodes V2 = {U1,-. uN) } with the splits desig- nating the top 20% of nodes by degree high-degree head node set Hi and the rest 80% as low-degree tail node set To following the Pareto principle (also known as the 20/80 rule) (Sanders, 1987). The local node-level topology-imbalanee is set the ratio of the average node degree of the head training node set to the average node degree of the tail training node set, i.e.
PL. Ed()), Hh
P
T. Ed(o),uETT
(B.2)
where d(() denotes node degree and we require d(v) 2 1. Node degrees frequently exhibit a long-tail tail distribution. Head nodes, which have high degrees, benefit from richer structural information, resulting in superior performance in downstream tasks such as node classifica- tion. In contrast, tail nodes with low degrees possess limited topological information, which hampers their performance (Liu et al., 2020; 2021).
Global Imbalance. The global imbalance is facilitated by two aspects: and Squashing (Sun et al., 2022b). Under-Reachin the influence from labeled nodes decays with the topology distance, resulting in the nodes being far away from labeled nodes lacking supervision information. Over-Squashin to the phenomenon of the supervision information of valuable labeled nodes being squashed when passing across the narrow path together with other useless information. The global node-level applogy-imballan
refers to the phenomenon that
refers
ratio is set the 10x negative logarithm of the absolute value of the product of the Reaching Coefficient (RC) and the Squashing Coefficient (SC) (Sun et al., 2022b), i.e..
p -10 log RC SSI..
(B.3)
o Reaching Coefficient (RC) is the mean length of the shortest path from unlabeled to the labeled nodes of their corresponding classes, iee.,
11
log PP spp (1 U₁)]
RC
Σ E
(B.4)
Vu
log Dg
VVVV
where D denotes the nodes in V2 whose label is y Pap (vi, 05) denotes the shortest path between U; and 0j. and |Po, vz)l denotes its length, and De is the graph diameter. o Squashing Coefficient (SC) is the mean Ricci curvature (Ollivier, 2009) of edges on the shortest path from unlabeled the labeled nodes of their corresponding classes, ie.,
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Table B.2: Number of nodes for each class in node-level datasets under different p.
Dataset
# Node for Each Class
p= 20
9, 15, 24, 80, 100
Cora [65]
p= 100
2, 6, 14, 17, 31, 200
p= 20
7. 13, 25, 46, 99, 140
CiteSecr [65]
100
2. 5, 12, 31, 80, 200
20
77. 354, 1540
PubMed [65]
100
17, 254, 1700
= 20
20, 28, 39, 55, 76, 107, 150, 208, 297, 400
Computers [46]
= 100
5, 9, 15, 25, 43, 71. 119, 199, 394, 500
p= 20
13, 21, 32, 49, 75, 116, 194, 260
Photo [46]
p
3, 7, 13, 26, 51, 98, 262, 300
47, 51, 56, 60. 65, 70, 76, 83. 89, 97, 105, 113, 123, 133, 144, 156, 168, 182, 197, 213, 231.
20
250, 271.
317. 343, 371, 401, 434, 470, 509, 550, 596, 645, 697. 755, 817. 940
ogbn-arXiv [14]
13, 15. 17, 19, 22, 25, 28. 32, 36, 41, 52, 59, 66, 75, 85, 96, 108. 122, 138. 156, 176, 199,
100
225, 254, 286, 323, 365, 412, 465, 525, 593, 669, 756, 853, 963, 1154, 1268, 1300
20
6, 12, 27, 60, 120 5, 25, 94, 100
Chameleon [44]
= 100
20
14, 29, 62, 135, 280
Squirrel [44]
3, 15, 171, 300
P = 20
20, 43, 91, 206, 400
Actor [39]
P
5. 52, 187, 500
Loxr EenrEPep(Han) Pep(mann)) Ric(u,, 1t)
Σ SC = VVll neVo (o:))
Σ
(B.5)
(Pp 0z)l
Uy (v))
where Ny, (w:) denotes the labeled nodes of class y, that can reach the node us -ic(.:)) denotes the Ricci curvature, and [Pep(u,, uy)l denotes the length of shortest path between node pair n and v/y.
Graph-Level Topology- Imbalance. Given a set of labeled graphs G, = (91, ,.,.. 99v) } with the splits designating the top 20% of graphs by graph size (the number of nodes) large-size head graph set Hg and the rest 80% as small-size tail graph set Tg following the Pareto principle (20/80 rule) (Sanders, 1987). The imbalance ratio is set to the ratio of the average graph size of the head graph set to the average graph size of the tail graph set, ie.,
H4 Σ 9.1.9. E Hg
(B.6)
3, TTg
The complex connections within graphs result in topology imbalances across different graphs. This imbalance frequently appears as variations in graph sizes. Generally, graphs with larger sizes tend to be more expressive and thus produce better performance compared to smaller counterparts. This dynamic can introduce bias in applications like molecular or protein prediction.
B.2 MANIPULATED CLASS- IMBALANCED DATASETS FOR NODE CLASSIFICATION
Dataset Settings. We perform the node classification task semi-supervised on 9 manipulated class- imbalanced datasets, where the train/val/test split satisfies the ratio of 1:1:8. Specifically, to construct the long-tailed distribution of the number of training nodes concerning varying imbalance ratio defined in Equation B. we assume that the number of nodes each class the training set grows exponentially, i.e., |Ce+al
sa(C,), where i is the class index, |C,| is the number of i-th indexed class training samples and μ E (0,1) is the coefficient. Therefore, given the total number of nodes in the training set and p. the number of nodes used for training in each class can be calculated deterministically. All nodes other than those used for training and validation are assigned to the test set. To provide thorough evaluation, i.e., the class-balances setting (p- = I and each class has an equal number of training nodes), the dass-imbalanced setting (p = 20), and the extreme hass-imbalanced setting (p 100)..
consider three typical situations in IGL- IGL-Bench,
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CheSoar
60+
120
100
19
20
24
Clast Eadex
Class Endex
Class Tndex
Class Tades
Compuionx
Compuiee (P
1190
403
139
1330
10:0
-00
200
250
Class Iades
Class Eadex
Class Tados
Class Eados
(.
(
230
Netio
of Notio
100
Maden
50
22
Class Bidex
Class Iadex
Class Fadex
Sqgurel
Squtael pM
(
Artoot
350
400
250
220
170
150
100
102
Clacs Kalee
Clacc
ClasTalke
ogto-
opt (p 108)
1200
209
200
Cluy fades
C
Figure B.1: Visualizations of the distribution of the number of nodes in the training sets for 9 benchmark datasets with different imbalance ratios. Note that, we calculate the imbalance ratio for the agbn-arXiv (Hu et al., 2020) by the ratio between the number of nodes/graphs in the majority class and the number of nodes/graphs in the sub-minority class due to insufficient training nodes in some classes.
Dataset Preview. We present a visualization of the distribution of the number nodes in the training sets for each dataset in Table B.2 and Figure B. It clearly reveals that the distribution follows long-tail pattern. Notably, as the parameter P increases, the number of nodes decreases more sharply, accentuating the long-tail tail effect. The higher the value of p, the more pronounced decline in node numbers, resulting in an even longer and more extended "tail". This trend indicates a significant imbalance, where few classes highly prevalent while the majority sparsely represented.
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Table B.3: Statisties of the manipulated local topology-imbalancer datasets (training) for node classification. The number of nodes for each class is equal (class-balanced), and the imbalance ratio p is the ratio between the average degree of the head nodes and the average degree of the tail nodes.
#Nodes
# Head Nodes
#Tail Nodes
Avg. # Degree
Avg. # Degree
Imbalance
Dataset
Level
per Class
per Class
per Class
(Head Nodes)
(Tail Nodes)
Ratio
Low
35
5.64
2.84
1.98
Cora [65]
Mid
39
31
8.96
2.74
3.27
High
27
13.53
6.74
Low
6
49
4,47
1.83
2.44
CiteSeer [65]
Mid
55
12
43
6.78
1.62
4.18
High
18
37
9.61
1.17
8.21
Low
66
591
8.58
2.08
4.12
PubMed [65]
Mid
657
132
525
15.04
1.83
8.23
High
198
459
22.93
1.51
15.23
Low
21.85
2.66
Computers [46]
Mid
138
99.77
20.23
4.93
High
96
133.14
12.98
10.26
Low
10
86
48.96
19.56
2.50
Photo [46]
Mid
96
20
76
84.03
17.50
4.80
High
30
66
116.33
13.13
8.85
Low
42
381
21.56
8.22
2.62
oghn-arXiv [14]
Mid
423
84
339
40.75
5.10
7.99
High
126
297
56.08
3.80
14.74
Low
41
12.12
4.23
Chameleon [44]
Mid
36
108.28
12.20
8.88
High
31
159.44
9.29
17.16
Low
93
162.02
22.35
7.24
Squirrel [44]
Mid
104
22
82
328.33
21.71
15.13
High
33
71
496.67
14.75
33.67
Low
15
137
15.24
4.66
3.27
Actor [39]
Mid
152
30
122
26.77
4.11
6.52
High
45
107
37.93
3.02
12.56
B.3 MANIPULATED LOCAL TOPOLOGY-IMBALANCER DATASETS FOR NODE CLASSIFICATION
Dataset Settings. We conduct the semi-sun cumisuupre node classification task on manipulated locally topology-imbalaneed datasets. The datasets are split into training, validation, and test sets with a ratio of 1:1:8. Local topology-imbal -imbllance is characterized by long-tailed distribution in terms of node degree. Following the Pareto principle (the 20/80 rule) (Sanders, 1987), we designate the top 20% of nodes by degree as high-degree (head) nodes, and the remaining 80% as low-degree (tail) nodes. High-degree nodes benefit from in downstream tasks, while low-degree nodes suffer from limited topological information, which hinders their performance. To evaluate local topology-imbalance, validation nodes according to the pre-defined splitting ratio (10%/10%) while ensuring an equal number of nodes per class for fairness. The remaining nodes are used for testing. To thoroughly assess the performance of the IGL algorithms, we create training sets with different imbalance ratios, as defined Equation B.2. These ratios depend on the proportion nodes selected from the head and tail sets. We repeat the node selection process multiple times, calculate the resulting imbalance ratios, and choose three groups of splits exhibiting significant variations in the imbalance ratio. These groups categorized Low, Mid, and High, based on their respective levels of local topology imbalance.
abundant structural information with superior performance
randomly select training and
Dataset Preview. We conclude the statistics of the manipulated local topology-imbalaneee datasets (training) for node classification in Table B.3. To guarantee a fair evaluation, we ensure the number of nodes for each class is equal to Low, Mid, and High roughly doubles, which can better simulate the various degrees of the imbalanced distribution of node degree.
We also observe that the imbalance ratio corresponding
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Table B.4: Statistics the manipulated global topology-imbalanee datasets (training) for node classification. The number of nodes for each class is equal (class-balanced), and the imbalance ratio P is the 10x negative logarithm of the absolute value of the product of RC and SC.
Imbalance
Cora
CiteSeer
PubMed
Computers
Photo
Chamelcon
Squirrel
Actor [39]
Split
Dataset
Level
[65]
[65]
[65]
[46]
[46]
[44]
[44]
RC
0.60
0.84
0.62
0.73
0.54
0.49
0.46
0.56
Low
SC
-0.62
-0.87
-0.63
-0.53
-0.71
p
4.23
4.62
3.02
4.70
4.87
RC
0.60
0.84
0.61
0.72
0.54
0.49
0.45
0.56
SC
-0.62
-0.81
-0.87
-0.63
-0.67
-0.53
-0.71
p
4.26
4.66
3.03
1.99
4.71
4.87
6.22
4.03
0.60
0.84
0.72
0.54
0.48
0.45
SC
-0.87
-0.53
-0.71
p
4.26
4.69
3.03
2.00
4.72
4.93
6.23
4.02
0.60
0.83
0.72
0.54
0.48
SC
-0.87
-0.54
-0.70
p 4.31
4.75
3.04
2.01
4.73
4.96
6.21
4.08
0.59
0.83
0.72
0.54
0.46
SC
-0.62
-0.40
-0.81
-0.87
-0.63
-0.67
-0.53
-0.71
P 4.35
4.77
3.04
2.02
4.73
5.11
6.41
4.10
Mid
RC 0.59
0.81
0.61
0.72
0.54
0.46
0.43
0.55
SC
-0.62
-0.41
-0.81
-0.87
-0.63
-0.67
-0.54
-0.70
P 4.35
4.80
3.05
2.03
4.74
5.11
6.36
4.16
RC 0.59
0.81
0.61
0.72
0.54
0.45
0.41
0.54
SC -0.62
-0.40
-0.81
-0.87
-0.62
-0.67
-0.53
-0.70
p 4.35
4.87
3.08
2.04
4.75
5.20
6.56
4.16
RC
0.58
0.80
0.60
0.72
0.54
0.44
0.41
0.54
8
SC
-0.63
-0.40
-0.81
-0.87
-0.62
-0.67
-0.54
-0.70
p 4.38
4.94
3.11
2.04
4.76
5.32
6.63
4.19
RC 0.58
0.80
0.60
0.72
0.54
0.42
0.40
0.54
9
SC
-0.63
-0.40
-0.81
-0.87
-0.62
-0.67
-0.53
-0.70
p 4.39
4.96
3.12
2.05
4.77
5.47
6.73
4,20
RC 0.58
0.80
0.59
0.72
0.53
0.41
0.41
0.54
High
10
SC
-0.62
-0.39
-0.81
-0.87
-0.62
-0.68
-0.52
-0.69
4.43
5.05
3,16
2.06
4.77
5.51
6.79
4.24
B.4 MANIPULATED GLOOATT. TOPOL.OGY-IMRALANCCE DATASETS FOR NODE CLASSIFICATION
Dataset Settings. We conduct semi-supervised node classification task on 8 manipulated globally topology hopology-imbalanced imbalanced datasets. We seleet 10% nodes for training and 10% nodes for validation. For fair comparison, we assign the same number nodes for each class to guarantee the when evaluating the global topology-imbalance issue. The remaining nodes used for testing. The global topology-imbalan phenomenon, which are quantified with the metrics of the Reaching Coefficient (RC) and the Squashing Coefficient (SC). Considering that RC and SC' reflect two aspects of the causes of global topology-imbalance simultaneously, and both variables change monotonically, the negative logarithm of their product is used to define the imbalance ratio according to Equation B.3 (since RC' is positive and SC is negative, the purpose of 10x and taking the negative logarithm variation of the imbalance ratio). Note that, larger RC' means better reachability and larger SC means lower squashing. Consequently, the lower the degree of global topology-imbalane randomly generate 100 groups of training splits and calculate the imbalance ratio for each. We sclect 10 groups with the minimum, maximum, and uniformly varying imbalance ratios within the range to simulate the change in the degree of global topology imbalance from High to Low.
issue is facilitated by both the under-reaching and over-squashing
amplify the observable
ratio. We
Dataset Preview. We conclude the statistics the manipulated local topology hopology-imbalanee datasets (training) for node classification in Table B.4. To guarantee fair evaluation, ensure the number of nodes for each class equal colass-balancedd It can be observed that as the imbalance degree increases from low to high, the imbalance ratio also increases from small to large.
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Table B.5: Statistics of the manipulated class-imbalanced datasets for graph classification. The imbalance ratio for the graph-level class-imbalance problem is set to the ratio between the number of graphs in the majority and the number of graphs in the minority class, The number of graphs for each class is equal in the validation set for fair evaluation.
# #Graphs (val.)
#Graphs (Majority Class)
#Graphs
Imbalance
Dataset
Task
Level
per Class
(Minority Class)
Ratio p
Balanced
17
17
1.0 (5:5)
PTC-MR [1]
Binary
Low
17
23
2.3 (7:3)
High
30
(9:1)
Balanced
216
216
1.0 (5:5)
FRANKENSTEIN (1]
Binary
Low
216
302
130
(7:3)
High
388
(9:1)
Balanced
55
(5:5)
PROTEINS [2]
Binary
Low
55
77
(7:3)
High
99
(9:1)
Balanced
58
1.0 (5:5)
D&D [47]
Binary
Low
58
80
(7:3)
High
104
12
(9:1)
Balanced
50
50
1.0 (5:5)
IMDB-B [5]
Binary
Low
50
70
30
(7:3)
High
90
10
(9:1)
Balanced
100
100
1.0 (5:5)
REDDIT-B [64]
Binary
Low
140
(7:3)
Iligh
180
20
9.0 (9:1)
ogbg-molhiv [14]
Binary
400
38,884
643
60.4
Balanced
167
167
Multi-
COLLAB [22]
Low
167
380
19
20
Class
High
400
100
B.5 MANIPULATED LABALNED DATASETS FOR GRAPII CLASSIFICATION
Dataset Settings. We conduct the graph classification task on the manipulated hlassiiballanced graph datasets, which are split into training, validation, and test sets with ratio of 1:1:8. We also evaluate IGL. algorithms on the naturally imbalanced ogbg-molhiv dataset, consisting of a large number of graphs. Our manipulations involve three different types of processing methods. For O balanced datasets with binary classification, we randomly sample 10%/10% graphs for training and validation, and the rest are for testing to ensure the sufficiency of the minority class instances in both training and validation set given the skewed imitative data distribution. According to Equation B. the imbalance ratio for the graph-level of graphs in the majority and the number of graphs in the minority class. To construct graph datasets with different imbalance ratios, we select the class with a larger number of graphs as the majority class, and the remaining class the minority class. We then create training datasets with different imbalance ratios by adjusting the training sample ratios to 9:1 (p = 9.0), 7:3 (p = 2.3), and 5:5 (p 1.0, dass-balanced), while ensuring that the number of training samples constitutes 10% of the total. In the validation set, an equal number of samples are allocated for each class for fairness. All remaining samples are then assigned the test set. For imbalanced dataset with binary classification, to make validation/test sets balanced, we sample the same number of graphs from each class for validation/test sets. Then, the remaining graphs are assigned to the training set. For O multi- class classification, situations are similar to manipulations defined in Section B.2. We hypothesize that the number of graphs in each class within the training dataset multiplies exponentially. Given the total number of graphs in the training dataset and p. the number of graphs allocated for training in each class can be determined with certainty. Any graphs not allocated for training or validation assigned to the test set. For thorough performance evaluation, consider three scenarios within BBrch: a class-balancee scenario (p = 1), a maas-imballaced scenario (p = 20), and an extreme class- imbalanced scenario (p 100).
insalimma problem set to the ratio between the number
Dataset Preview. We conclude the statistics of the manipulated inaalaimae datasets for graph classification in Table B.5. It can be observed that the constructed datasets not only evaluate the ideal baass-balancdd (p = 1) scenario but also comprehensively assess the performance of IGL algorithms under the general class-imbalanced and extremely class-imbalanced conditions.
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Table 6.6: Statistics of the manipulated applogy-immalaneee datasets (training) for graph classifica- tion. The number of nodes for each class is equal (laas-bbllanedd,, and the imbalance ratio p is the ratio between the average size of the head graphs and the average size of the tail graphs.
GGraphs
/ Heed Graphs A Tail Graphs
Avg. #
Avg. #Size
Imbalance Ratio p
Dataset
Level
per Class
per Class
per Class
(Head Gruphs)
(Tail Graphs)
Low
29.50
18,40
1.60
PTC-MR [1]
Mid
34.25
11.80
2.90
High
56,00
11.37
4.93
Low
33.09
21.19
1.56
FRANKENSTEIN [1]
Mid
217
22
195
32.43
13.78
2.35
High
77.55
13.78
5.63
Low
93.50
45.81
2.04
PROTEINS [2]
Mid
50
90.25
22.26
4.05
High
276.00
22.76
12.13
Low
548.00
350.58
1.56
D&D [47)
Mid
59
53
524.83
207.70
2.53
High
1765.00
198.11
8.91
Low
37,50
22.92
1.64
IMDB-B [5]
Mid
34.30
16.29
2.11
High
70.30
15.81
4.45
Low
1180.75
423,23
2.79
REDDIT-B [64]
Mid
100
10
90
1097.75
223.04
4.92
High
2442.70
222.73
10.97
Low
37.69
23.12
1.63
ogbg-molhiv [14]
Mid
200
20
180
41.87
15.86
2.64
High
89.30
15.64
5.71
Low
141.41
80.14
1.76
COLLAB [22]
Mid
167
17
150
147.22
50.04
2.94
High
309.41
50.77
6.09
B.6 MANIPULATED TOPOLOGY- DATASETS FOR GRAPH CLASSIFICATION
Dataset Settings. We conduct the graph classification task the 7 manipulated aopology-imbalane graph datasets. For 6 balanced datasets, we divide them into training, validation, and test sets with ratio of 1:1:8. To ensure fairness, maintain an equal number of graphs per class within each set, achieving a class-balanced scenario. For the naturally imbalanced ogbg-molhiv dataset, considering that one category contains small number of graphs, we randomly sample a specified number of graphs from each category for training and validation, reserving the remainder for testing. Equation B.6 defines the imbalance ratio to be the ratio of the average graph size in the head graph set to the average graph size in the tail graph set. Specifically, the head graph set consists of the top 20% of graphs terms of size (measured by the number of nodes each graph contains), while the remaining 80% comprise the tail graph set (Sanders, 1987). Typically, larger graphs are more expressive due to their complex structures and richer information content. This expressiveness often translates to improved performance in graph classification tasks compared to smaller graphs. However, this advantage can also introduce biases applications such as molecular or protein prediction, where larger graphs might inherently contain more predictive features, overshadowing the smaller graphs. We create training datasets with varying degrees imbalance. The degree of imbalance is manipulated by altering the proportion of graphs selected from the head and tail sets. We select graphs multiple times, each time computing the resulting imbalance ratios. From these computations, identify three distinct sets of splits that exhibit significant variations in imbalance levels. These sets are categorized and labeled as Low, Mid, and High to reflect their respective levels of local topology imbalance. By systematically varying the imbalance levels, we aim to simulate diverse real-world scenarios. This approach allows us to rigorously test the robustness and adaptability of IGI algorithms under different degrees of topology imbalance. Ultimately, this comprehensive evaluation provides deeper understanding of the performance of IGL algorithms across datasets with varying characteristics, highlighting their strengths and potential areas for improvement.
Dataset Preview. We conclude the statistics of the manipulated class-imbalanced datasets for graph classification in Table B.5. To guarantee a fair evaluation, we ensure the number of graphs for each class is equal balanced....d... We also observe that the imbalance ratio corresponds to Low, Mid, and High roughly doubles, which can better simulate the various degrees of the imbalanced distribution of graph sizes.
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Table C.I: Different evaluation metrics for each algorithm in original papers.
Algorithm
Accuracy
Balanced Accuracy
Macro-F1
AUC-ROC
Others
DRGCN [48]
DPGNN [57]
Weighted-F1, Micro-FI
ImGAGN [42]
Precision, Recall
GraphSMOTE [70]
GraphENS [37]
/
GraphMixup [60]
LTE4G [67]
G-Means
TAM [49]
TOPOAUC [8]
Weighted-F1
GraphSHA [24]
DEMO-NET [59]
meta-tail2ve [30]
Micro-F1
Tail-GNN [31]
Micro-F1
Cold Brew [72]
RawlsGCN [19]
Bias
GraphPatcher [17]
ReNode [7]
Weighted-F1
PASTEL [52]
Weighted-F1
HyperIMBA [12]
Weighted-F1, Micro-FI
G'GNN [58]
Micro-FI
Topolmb [71]
DataDec [68]
Micro-F1
ImGKB [54]
Recall
SOLT-GNN [32]
C DETAILS OF THE EXPERIMENTAL SETTINGS
C.I GENERAL EXPERIMENTAL CONFIGURATIONS
The number of training epochs for optimizing all IGL algorithms is set to 1000. We adopt the early stopping strategy, i.e., stop training if the performance on the validation set does not improve for 50 epochs. All parameters appropriate learning rate and weight decay for the best performance on the validation split. We randomly all the experiments 10 times, and report the average results with standard deviations.
randomly initiated. We adopt Adam (Kingma & Ba, 2015) with an
C.2 EVALUATION METRICS
To perform an unbiased evaluation, we summarize all the metrics used in the original papers of the algorithms Table C. We can conclude that, Accuracy (Acc.), Balanced Accuracy (bAcc.), Macro-F1, and AUC-ROC are four commonly used metrics for evaluating imbalanced graph learning performance. Though metries like Weighted-F1 and Micro-F1 are also popular for evaluation, their difference lies in considering the imbalance between classes. However, this aligns similarly with the difference between Accuracy and Balanced Accuracy, so we have not taken metrics like Weighted-Fi and Micro-F1 into the evaluation. However, all experiment settings, it is easy to include more metrics in our benchmark in a short updating time for all algorithms under various experiment settings.
have saved the weights for each algorithm under
We briefly introduce and analyze the evaluation metrics employed to assess the performance of IGL algorithms including Accuracy (Acc.), Balanced Accuracy (bAcc.), Macro-F1, and AUC-ROC.
29

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Accuracy (Kipf & Welling, 2016). It reflects the ratio of correctly predicted instances the total number instances. It is formally defined as:
TP + TN
Accuracy TP+ + FP + FN'
(C.1)
where TP denotes true positives, TN denotes true negatives, FP denotes false positives, and FN denotes false negatives. Advantages: Accuracy is simple and case of interpretation. Further, provides an immediate, overall performance measure of the algorithm. @ Disadvantages: In the imbalanced datasets, Accuracy can be misleading as it tends to favor the majority class, and fails to account for the distribution of classes, underrepresenting the performance of minority classes.
Balanced Accuracy (Brodersen et al., 2010). Balanced Accuracy adjusts the conventional Accuracy to account for class imbalance. It is the average of recall obtained in each class. For multi-class classification, it is defined as:
N
TP: TP. + FN.
Balanced Accuracy
(C.2)
N
where N is the number of classes. 1 Advantages: Accuracy accounts for class imbalance, providing a more equitable evaluation, and it reflects performance across all classes more accurately than standard accuracy. @ Disadvantages: May be sensitive to noise and outliers, particularly in minority classes. In addition, it is potentially less intuitive to interpret compared to simple accuracy.
Macro-F1 (Xia al., 2014). The Macro-F1 score is the harmonic mean of precision and recall, calculated independently for each class and then averaged. It is expressed as:
Macro-F1 1 N
2. Precision, Recall;
(C.3)
Precision, + Recall,
where Precision; TP+FF. and Recall, TF. F.N.
Advantages: Macro-F1 emphasizes both precision and recall, ensuring consideration of both false positives and false negatives. Moreover, it provides a balanced view of the classification performance across all classes. @ Disadvantages: can be disproportionately affected by very small classes and does not account for the prevalence of different classes.
TPP
TP.
AUC-ROC (Bradley, 1997). AUC-ROC (Area Under the Receiver Operating Characteristic Curve) measures the area under the ROC curve, which plots the true positive rate (recall) against the false positive rate (fall-out) various threshold settings. For binary classification, it is defined as:
- AUC-ROC- - 1 ROC(t) dt.
(C.4)
For multi-class problems, an average of the AUC-ROC scores for each class against the rest can be employed. O Advantages: AUC-ROC evaluates the algorithm's 's performance across all possible classification thresholds. @ Disadvantages: It is computationally intensive, particularly for large datasets. Further, it does not provide clear threshold for decision-making. focusing instead overall ranking performance.
Analysis. When evaluating node-level and graph-level tasks under class-imbalance and topology- imbalance conditions, selecting the appropriate evaluation metric is crucial. O Accuracy is often unsuitable for imbalanced scenarios due to its tendency to favor the majority class, potentially providing a false sense of model performance when minority classes are present. Accuracy and Macro-Fl are more appropriate for imbalanced datasets as they offer a more equitable assessment of performance across classes. Macro-F1, in particular, is informative in tasks where both precision and recall are critical. O AUC-ROC advantageous ranking- based scenarios and for evaluating models across different thresholds. Its robustness class imbalance is beneficial, though its interpretation can be less straightforward in multi-class problems.
Balanced
In summary, while no single metric is universally optimal, a combination of these metrics can provide a comprehensive evaluation of imbalanced graph learning algorithms. Accuracy offers a general overview, while Balanced Accuracy and Macro-F1 provide insights into class-specific performance. ROC- on the other hand, offers a threshold iithoodddddeeeedeent evaluation, particularly useful in highly imbalanced scenarios.
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Published as a conference paper at ICLR 2025
Table C.2: Hyperparameter search space for node-level class-imbalanced IGL algorithms.
Algorithm
Hyperparameter
Search Space
dropout
0.2, 0.3, 0.4, 0.5, 0.6 5e 5e-5. 5e 4, 5e-3 500, 1000, 2000
weight decay
General Settings
numher of max training epochs
learning rate
0.005, 0.0075, 0.01, 0.015
number of layers
1, 32, 64,
GCN [21]
hidden size
DRGCN [48]
for loss trade-off
0.5, 0.6, 0.7, 0.8, 0.9
A1 for Lest,
1, 10
DPONN [57]
A for Lxd,
1, 10
threshold for the hard pscudo label
0, 2,4,3,
A for minority nodes ratio
0.2, 0.3, 0.4, 0.5, 0.6 20, 30, 40, 50, 60
ImGAGN [42]
A for discriminator training steps
GraphSMOTE [70]
Ledge
le-6, 2c-6, 4c-6
number of warming up epochs k for feature masking
1,5 1,5, 10 1,2
GraphENS [37]
I temperature
for the focal loss
0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 0, 1,2
LTE4G [67]
y for shape controlling
é for the class wise temperature
0.8, 1,2 0.25, 0.5, 1.5, 0.125, 0.25, 0.5
for the ACM term of node
TAM [49]
for the ADM term of node
the base model
GraphENS [37], ReNode [7]
GraphSHA [24]
sampled 3-distribution
$01,100,, $1,100
C.3 HYPERPARAMETER
We meticulously optimize hyperparameters to guarantee rigorous and unbiased assessment of the integrated IGL methods. In cases where the original paper or source code for a specific algorithm lacks guidance hyperparameter selection, we perform the hyperparameter tuning through Bayesian search on the Weights Biases (wandb) platform*. The hyperparameter search space for IGL algorithms is detailed in Table C.2 (for node-level class-imbalanced IGL algorithms), Table C.3 (for node-level topology-ing topology-imbalanee imbalanced IGL algorithms), and Table C.4 (for graph-level slass-imbalanced IGL algorithms). For interpretations of these hyperparameters, please consult the respective papers. More detailed and comprehensive hyperparameter configurations for all algorithms are accessible within our publicly released GitHub package.
and aopoloyy-ibbllnee
"https://wandb. /
31

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Published as a conference paper at ICLR 2025
Table C.3: Hyperparameter search space for node-level appoloyyiimbllnned IGL algorithms.
Algorithm
Hyperparameter
Search Space
dropout
0.2, 0.3, 0.4, 0,5, 0.6
weight decay
0, Se-6, 5e-5, 5e-4, Se-3
General Scttings
number of max training epochs
500. 1000, 2000
learning rate
0.005, 0.0075, 0.01, 0.015,
number of layers
1,2,
GCN [21]
hidden size
32, 64, 128
I for Lm for La
0.01, 0.001
Tail-GNN [31]
0.1, 1.0
a for mixing coefficient
0.01, 0.1, 0.5, 0.9, 0.99
Cold Brew [72]
number of propagations
10. 20, 50, 100, 200
a for the focal loss
0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 0,
LTE4G [67]
for curve shape controlling
RawlsGCN [19]
or for probability scalar
0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9
batch size
4, 8, 16, 64
number of accumulation steps
16, 32, 64
GraphPatcher [17]
number of patching steps
3,
augmentation length
0.1, 0.2, 0.3
PageRank teleport probability
0.05, 0.1, 0.15, 0.2
ReNode [7]
lower bound of rewcighting
0.25, 0.5, 0.75
upper bound of rewcighting
1.25, 1.5, 1.75
@ for the class-wise temperature
0.8, 1.2 0.25, 0.5, 1.5,
TAM [49]
for the ACM term of node
8 for ADM term node
0.125, 0.25, 0.5
A1 for structure mixing
0.7, 0.8, 0.9 0.7, 0.8, 0.9
PASTEL [52]
A for structure mixing
Table C.4: Hyperparameter search space for both the graph-level class-imbalanced and topology- imbalanced IGL algorithms.
Algorithm
Hyperparameter
Search Space
dropout
0.2, 0.4, 0.5, 0.6 0, 5e-6, 5e-5, 5e-4, 5e-3 500. 1000, 2000
weight decay
General Settings
number of max training epochs
learning rate
0.001.0.005.00100022555000
number of layers
2. 4 32, 64. 128
GCN [21], GIN [63]
hidden size
k for the number of neighhoring graphs drop edge ratio mask node ratio
1e-5 1e--,,555 1,2,
G:GNN [58]
5e-5_le-4,55-44ee--.ee
Topolmb [71]
a for LRE
0.2, 0.3. 0.4, 0.5, 0.6
compression coefficient
0.3. 0.4, 0.5, 0.6
ImGKB [54]
ls for the number of neighboring graphs
2, 6, 8, 10
a for loss trade-off
0.1, 0.15, 0.3
SOLT-GNN [32]
for goode
0, 0.5, 1.5,
for Laubg
0, 0.5, 1.5,
32

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Published as a conference paper at ICLR 2025
C.4 COMPUTATION RESOUCES
We conduct the experiments with the following resources and configurations:
Operating System: Ubuntu 20.04 LTS.
CPU: Intel(R) Xeon(R) Platinum 8358 CPU@2.60GHZ with 1TB DDR4 of Memory.
GPU: NVIDIA Tesla A100 SMX4 with 40GB of Memory.
Software: CUDA 10.1, Python 3.8.12 PyTorch (Paszke et al., 2019) 1.9.1, Py PyTorch Geomet- ric (Fey & Lenssen, 2019) 2.0.1.
D ADDITIONAL EXPERIMENTAL RESULTS
D.I ADDITIONAL RESULTS FOR ALGORITHM EFFECTIVENESS (RQ1)
D.1.1 EFFECTIVENESS OF NODE-LEVEL
ALGORIHTM
Table D.I: Accuracy score (% + standard deviation) of node classification on manipulated class- imbalanced graph datasets with changing imbalance levels over 10 runs. denotes out of memory or time limit. The best results are shown bold and the runner-ups are underlined.
Algorithm
Cora
CiteSeer
PubMed
Computers
Photo
ogba-arXiv
Chameleon
Squirrel 0.22
Actor 0.22
0.81
0.74
0.80
0.78
0.82
0.65
0.23
1 (Balanced)
GCN (bb.) [21]
80.41
66. 36.399
82,88
79. 29.2293
88. 38.300
45.92a0.8
26.76
21 16.46683
23
DRGCN [48]
77.78s1.2
66.99a1.7
81.37a2.96
63.71=26.44
85.67a093
33.81
24.90an.4
19
DPGNN [57]
74.20~247
62.07
80,96-1.00
15-15-
87.58+227
32.06+241
25.00+1.22
22
ImGAGN [42]
80,58
66.27am.0
82,78.0.1
16.67+1
86. 37.6240:37
29
21.614034
22
GraphSMOTE [70]
78.92a048
65.50a042
81.85
79.4640.00
86. 89
25.05#201
21.32:012
25 25.96
GraphENS (37)
80.41
66.42sa..6
82.87
78.71an.8
88.63x1.4
46 48.68
26.76
21 46:0877
23.07
Grxph [60]
79.30=0.54
69.95x1.00
83.85-0.11
82.16:1.8
90.5661335
43.88-1.02
35.05+034
24.59.0.32
24.29.1.16
LTE4G [67]
80,48s1.12
67.77a2.25
84.2720.30
74.23s4.72
88.482338
35.7
24.622n47
24.88a1.11
TAM [49)
81.33
66. 66.2620.52
74.56e0.78
78.76an.7
88.4921.57
46 66.6620.57
28.56x1.24
21.512094
23.54a0.50
TOPOAUC [8]
83.69.0.32
73.41...46
69.79x3.93
85.2..2.3
37.14:n95
25.24:046
26.25ai.22
GraphSHA [24]
80.41
66.40se.w
82.87
78.88
88.61a499
47.32a0.3
26. 26.76s189
21.462037
23.07a0.8
20 (Low)
GCN (bb.) [21]
76.36=0.13
52.96
60.57a0.19
75.06201.0
69. 80.6.1
59.83
26.352024
17.1620.17
24.06a0.14
DRGCN [48]
71.35-0.7
55.22+1.8 k2
62.59-460
67.71+3.00
85.6745
26.40+0
17.11-081
25.03-0:3
DPGNN [57]
72.91-396
56.7840.23
81.87-030
68.694862
81.6649
30.58+1
21.66+1 25.35-148
ImGAGN [42]
73.48=307
05.29
12.16
74.92+187
83. 10x343
24.38
18.75+180
24.54
GraphSMOTE [70)
77.21
$3.55a095
71.25a027
76.04s1.5
89.07s1.12
27.23s021
16.79an.44
25.08a0.31
GraphENS [37]
79.34=049
61.98s076
80.84=6.17
80.72
53.23-n.52
24.34+1
20.05
25.03:0.38
GraphMixup [60]
79.88=0.33
62. 66.0.0
75.942009
86.152n477
89.69an33
56.08a0.1
20.95an.40
17.8329322
24.75a0.77
LTE4G [67]
80.53
64 64.48s1.56
83.02a033
39.35s1.99
87.94x182
31.91a034
19.37a9.11
25.43an.26
TAM [49)
80.69-027
64. 14.024
81.47a0.3
81.30an.53
90.35an.2
$3.49.n.54
23.27
21.17an95
24.53am.3
TOPOAUC [8]
83.34
69.03s1.33
50.85
83.724223
33.6021.51
21.38a105
169666
GraphSHA [24]
80.03
60.51
77.94.036
82.7
91.55an33
60.30am.1
23.73x197
20.05a161
23.59at.0
100 (High)
GCN (bb.) [21]
62.20+1.57
42.48.0.4
47.31-0.2
58.04+n.8
46.54x0.3
60.35-0.24
25.68+012
1..177n010
21.70
DRGCN [48]
61.99-246
45.69.1.0
49.80-4.3
66.02-1 48
73.58.5.4
25. 24.794044
23.03-0 15.32-045
DPGNN [57]
67.98
51.1023.06
76.29
70.04a8.56
87.70an34
18.82+1.5
23.91:1.0
22.37
ImGAGN [42]
66.16.354
53.60.1.32
64.03a062
66.89.4.29
74.92.5.99
23.72+285
17.30
24.
10
GraphSMOTE [70)
69.81-006
45.72.0.0
69.12-022
56.55.1 29
44.97x0.22
25 12
15.41sn.10
21.76an.11
GraphENS [37]
77.68=0.8
62.85
76.69
60.9920.66
90.3 90.31
54.1 320.49
26.26+242
20.65+230
20.67:247
GraphMixup [60]
70.01
49.6 99.6340228
63.472000
79.3442142
73.02+400
57.40
26.41an0s
15.75
23.39
LTE4G [67]
73.70=0:9
57.14
30.5841532
99.59
29.53
884880
16.184034
24.764042
TAM [49]
79.36-0.5
64.30 300.00
80.53em.8
85.775041
90.28
54.25
23.47
23.48
21.92ah.8
TOPOAUC [8]
76.97
67.3142.0
82.7443.10
30.662n
17.672129
25.35
GraphSHA [24]
78.66-0:46
57.6346.82
70.68-2.4
80.79x0
91.27+0
60.17-0.17
14.1
20.78-2.19
20.82-248
33

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Published as a conference paper at ICLR 2025
Table D.2: Balanced Accuracy score (% + standard deviation) of node classification on manipulated class-imbalanced graph datasets with changing imbalance levels over 10 runs. denotes out of memory or time limit. The best results are shown in bold and the runner-ups are underlined.
Cora
CiteSeer
PubMed
Computers
Photo
ogbu-arXiv
Chameleon
Squirrel
Actor
Algorithm
0.81
0.74
0,80
0.78
0.82
0.65
0.23
0.22
0.22
(Balanced)
GCN (bb.) [21]
79.98
62 62.0.0
83.13a006
87. 26
89. 89.70
45.93a0.56
28. 28.0421.00
21.472037
22.65a0:35
DRGCK [48]
77.20w0.8
63.05a082
82.22a2.10
73.23
88. 22,22
24.36.1.20
24.89an.45
23.33a0:3
DPGNN [57]
75.79.244
28.96
81.42a3.0
74.75a1000
88. 15
33.07a192
24.99a1322
22.13
ImGAGN [42]
80.20s041
62.55ao.3
83. 11a00
84. 64.200a336
88, 80anzy
79.65
21.61a0a:
22.57
GraphSMOTE [70]
78.04-0:4
62. 16x0.41
82. 116.14
80.07sn.54
28.89
26. 26.83x201
21.34:0.22
22.04:0.32
GraphENS [37]
79.98-063
62.65x0.00
83.12-0.0
86 26+0:1
89.85+064
45.98-0.49
28.04+
21.47-037
22.65-0:38
Grxph [60]
82.41
67.48+1.00
84.72.0.0
88.96-n
91,90.024
43.97-0.49
35 3x
24.5940.3
23.5040.52
LTE4G [67]
81,97s1.2
65. 15a2.07
85.21
83.5922.06
88. 43.3333..
35. 33.13
24.61an47
24.88a0.13
TAM [49]
80,98
62.99s0.26
77.26.0.22
86.06an.52
89.77a074
46.05=0.77
28. 82.826
21.51an94
22.93an45
TOPOAUC [8]
84.86-0.1
69.90.o.42
77.23
85.24
37.92:n68
25.23
25 25.68-041
GraphSHA (24)
79.98
62, 63
13.007
86.1 120.44
89.8
46.40.0.55
28.0421.60
21.472077
22.65
20 (Low)
GCN (bb.) [21]
69.17=026
47.61
52.40a0.15
40. 86.866777
49.8747.16
37.36.0.11
26.75
20.83
20.62an.10
DRGCN [48]
63.04
49.86at.00
56.40a191
43.9242.58
74. 72.9.5
26.794035
19.98.045
22.10
DPGNN [57]
67.64
51.34:2.1
81,94.185
36
82.20+9.18
30.72e1
26.52s1
37
ImGAGN [42]
67.78:346
67.34s1.14
73.92s082
78. 14x2.12
24.50x271
20.14:074
23.83a1.78
GraphSMOTE [70]
70.54-042
48.27
70.54-6:31
31.46+4.33
27.54+020
20.63-015
21.73-0.1
GraphENS [37]
78.54-0.5
76
79.47-6.37
86.0
90.2640024
41 4..77
24 14
21.03+100
25.64-0.49
GraphMixup [60)
72.63a0.9
56.7620.68
72.40a0.10
82.91an
81.21a0.4
39.67s0.6
31.21a036
20.81a025
21.68a0.6
LTE4G [67]
75.42=1.26
58.52a1.35
81 18.82222
72.29:3.00
87.99x1.34
32.00sn34
22.37a034
23.11a0.3
TAM [49]
80.29
81.20 20.88
19
90.19an21
41.94en.35
23.82a144
21.1
25.84a0.0
TOPOAUC [8]
79.98=0.33
63.6920.9
77. 77.02a2.60
85. 65.7921.62
33.87
23.17a0:0
24.24a024
GraphSHA [24]
17.11
56.9 76.98
75.18
77.04an.44
88. 28.83s
35.9220.8
24.17:216
21.03:100
22.54a0.52
100 (High)
GCN (bb)) [21]
47.96-5.6
38.66 38.6640:20
43.02-0.55
22. 834207
25.0640366
30.20-0.1
27.02+012
20.62.009
20.22-0 12
DRGCN [48]
19.11
41.40
44,87
35 80.00e 98
85
27.1
20.57:0:3
21 03.033
DPGNN [57]
58.09:337
46.01s271
74.95=1.0
76.51a7.76
85.55x1.77
29.74.2.15
25.88.125
21.18
ImGAGN [42]
57.01
18.70
55.56-0.44
60.84x6.50
29.88
26.76.295
19.81
22.21
GraphSMOTE [70]
58.9
41.60io.44
64.02-0:0
21 21.05
13.91+012
26.9 16.91.013
20.67-0.14
20.27-0.11
GraphENS [37]
73.61=013
58.08a0.99
73.62a0.43
85.72+n.42
90. 19.311
40.42=0.5
27.124261
22.032149
20.992143
GraphMixup [60]
56.43=0.99
44 24.633022
$7.8620.13
49.37anus
54.60x488
34.44=0.19
27. 27.93sm00
20.50en:15
21.25
LTE4G [67]
62.22a1.22
51.16at.21
67,8940050
72.49x2.92
83.28+119
29.692851
21.082029
22.79
TAM [49]
75.11
59. 10
78.98
85.77a0:41
90.20a024
40.61
23. 23.962194
22.74
21.97
TOPOAUC [8]
71.10=1.30
61.1342.02
25.1332223
32.102n42
21.22an:66
24.05
GraphSHA [24]
13
53.9240.0
65.28en.6
72.59k136
87.06
120.32
20+10.3
22.05
30.84
34

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Published as a conference paper at ICLR 2025
Table D.3: Macro-F1 score (% standard deviation) of node classification on manipulated class- imbalanced graph datasets with changing imbalance levels over 10 runs. denotes out of memory or time limit. The best results are shown bold and the runner-ups are underlined.
Cora
CiteSeer
PubMed
Computers
Photo
ogbu-arXiv
Chameleon
Squirrel 0.22
Actor 0.22
Algorithm
0.81
0.74
0,80
0.78
0.82
0.65
0.23
1 (Balanced)
GCN (bb.) [21]
78.26
61.83a078
82.03a0.16
68.40an.49
85.03a047
27. 27.50
23.99a195
18.802142
21 21.91
DRGCK [48]
75.46.097
62.65a1.09
80.4623.08
55.55
83,23a000
32.85a201
23.41an95
22.30ah.3a
DPGNN [57]
72.73
58.7742.6
80.49
55.27s1024
83.374287
30.06:306
21.67
17.38
ImGAGN [42]
78.60em01
61.70a0.4
81.96.0.12
66. 70.7001..0
83.79
26.45s253
18.76a124
21.55a0
GraphSMOTE [70]
77.03-042
61.20so.44
80,93=0.18
65.39
83.76xn:3
22.93
14.71+138
21.13
GraphENS [37]
78.26-0/1
61.8660.77
82.03-0.16
68.39.089
85.64x1.21
27.92-0.16
23.99+196
18.80+122
21.91+0:35
Graph [60]
77.54+073
82.92-6.10
70.81.092
86.84:n
26.14:0.88
33.76+0
23.78+076
22.25
LTE4G [67]
78.45s1.10
64.35a2.4
83,19.0.32
62.28a3.47
84.09a444
34.00sa67
23.45a031
22.75el.17
TAM [49)
79.34s061
61.95a0.33
74.23a0.77
68.53an72
85.48
27.93-0.22
25.40x186
18.43s2.12
22.10en.54
TOPOAUC [8]
81.95-036
69, 49.28
57.76x1
79.31x225
23.70k0.44
24.43-0.6
GraphSHA (24)
78.26
61.8420.7
82.02a0.15
68. 18.612
85.62a1.21
28.20
23.99s195
18.802162
21.91
20 (Low)
GCN (bb.) [21]
71.15-0.0
L3.71
45.71
39.1 1
48.9948.51
33.94
16.67
9.83e0.4
12.18
DRGCN [48]
64.43e1.52
47.50st:46
53.83e4.8
41.55+2.42
74.51
17.2240
11.01:038
16.43+0.57
DPGNN [57]
68.70.381
50.06e2.10
41.54.2.2
66.97a896
79.53+8
85
21.53
18.48e1.50
ImGAGN [42]
68.69:3.88
48.40a3.58
67.80s141
72.51s1
75.49
16.94x214
13.91s2.77
21.04:3.66
GraphSMOTE [70]
72.71-031
45.21
68.93-6a1
49.30+4.6
79.641098
18.72+026
8.36.0.6
16.26-0.44
GraphENS [37]
77.16-0.50
57.804096
79.71-634
77.89x0.9
88. 20
30.16-0.17
19.58.099
16.73+193
23.30-0
GraphMixup [60)
74.03a0.2
55.31a0.0
73.63a0.1
81.54an.88
80. 83an63
32.38-0.17
25.57a076
13.1720.9
18.35a0.54
LTE4G [67]
76.46=1.17
57.35a1.4
82.12.0:7
69 69.02+3.78
85.23
25. 35.96a
15.13a030
21.27a0.48
TAM [49]
78.83
12
80.75a0.15
78. 10snes
88. 16a030
30.30an.9
19.99a121
17.29
24.01a0.54
TOPOAUC [8]
80.61
62.95st.a1
67. 35
81.694235
29.0612.5
18.77a126
23.61a024
GraphSHA [24]
77. 77.6620.46
55.7620.5
76.17
75.43an.47
89.04an27
32.09
19.64x126
16.7321.73
20.36an:77
100 (High)
GCN (bb)) [21]
43.97=2.5
30.77+021
34.08-0.77
20.44+1.45
16.99.064
31.11
14.7940
8.27+a.17
9.01+006
DRGCN [48]
47.47
34.83-2.00
36.442129
33. 15.6001.15
68
15.02
8.83
12.38
DPGNN [57]
58.66:344
41.53,3.50
75.47=304
68.30s8.53
84.82+1.4
13.96x216
18.85-236
19.62s1.1
ImGAGN [42]
55.03=5.2
43.92-461
50.74-1.94
57.30
67.27
14.12
10.62.4.1
18.84-2.7
GraphSMOTE [70]
58,93-054
35, 40+0.1
63.27-0.19
17.90+ 20
16.34+004
15
9.31+0.9
9.05-a76
GraphENS [37]
72.09=0:2
56.58.0.00
74.3620.40
78.75an.50
88.53an25
30.6 30.89
20.80an64
17 17.962189
18.47:245
GraphMixup [60]
55.91=0.1
38.36
55.24m021
46.92an61
53. 53.544.772
33.18
20.02:a11
10.07:a17
14.46.0.7
LTE4G [67]
62.11
45.6741.91
66. 66.79415.4
70.80 70.80+2.70
83. 23.2442..7
21.02e1.0
10.61
17.8820.7
TAM [49]
75.07=0.7
57.6740.46
79.3420.21
78.97a0
88, 44
10.9
20.3721.49
20.28:148
21.33
TOPOAUC [8]
70.01
58,92a2.94
80. 23
24.41a1.51
13.624200
22.40za.40
GraphSHA [24]
23
61.99
64.66 64.66e1.00
72.46s1.10 10
88. 36
27.92a0.33
19.96s182
17.87s199
18.05
35

---

Published as a conference paper at ICLR 2025
Table D.4: AUC-ROC score (% + standard deviation) of node classification on manipulated class- imbalanced graph datasets with changing imbalance levels over runs. " denotes out of memory or time limit. The best results are shown in bold and the runner-ups underlined.
Cora 0.81
CiteSeer
PubMed
Computers
Photo
ogbn-arXiv Chamelcon
Squirre 0.22
Actor 0.22
Algorithm
0.74
0.80
0.78
0.82
0.65
0.23
1 (Balanced)
GCN (hh.) [21]
96.08-047
89.74-0.1
94.55-004
97.61-0.04
78.734
93.39ha.10
63.48-0.66
91.32-0
53.22.0.58
DRGCN [48]
95.01=0.30
89.32s0.2
94. 41
93,43a11115
98.49.u.12
64.9 44.933.449
55,40e0.3
54.2840.4
DPGNN [57]
93.84
86. 15
92.59
35.06e2:35
97. 85
63.30et 95
55.05s1.31
52.51
ImGAGN [42]
96.4920.7
89.97s0.13
04.522005
97. 12.0.15
98.53
64. 30.90
51.28
53. 53.662105
GraphSMOTE [70]
95.88-0.35
89.48-0.13
93.94-006
97.18-0.09
98 -8.6440..4
60.33-3.34
51.21+0.31
53.70+0.36
GraphENS [37]
96.08-047
89.74-0.1
94.55.0.4
97.67-0.07
98. 76
03.03
63.48-0.66
51,32+095
53.22.0.58
GraphMixup [60]
96.42:0:5
89,833999
95. 16
97.96-0.15
98. 49.00
92. 29.64400.0
63.164065
54,0140.1
53.8250.1
LTE4G [67]
96.54=039
89,00
95.61:005
95. 88
98. 1720.56
65 65.42:0.49
55,22s0.a 90
57.75
TAM [49]
96 85.00
89.7720.s
92.62a0.12
97. 69.69.000
98. 1
93.34
60.1 1=1.56
51,6740.78
51. 84.84
TOPOAUC [8]
97.56-004
91.89
91. 22.62.27
94. 11
67.70-0.58
55.43.0.0
57.17-0.59
GraphSHA [24]
96.08-0.7 89.74
04.54.004
97. 0.066
98. 76
93.50.00.6
63.4840.6
91,32+0.5
53.222..58
20 (Low)
GCN (hh.) [21]
95.04-008
86.5740.19
92.23-0.9
94.41-0.59
94.35-0.66
93.54.009
57.70+0.22
51.70+0ms
52.05-0.36
DRGCN [48]
92.68-0.30
84.92s06)
34.0440.3
84.8.4.05
29.
56.19.0.6
49. 49.42.008
55.20+028
DPGNN [57]
92.41s108
81.04:1.4
93.24s1.77
05.03a1.9
96.30a2..0
60.45s2.11
55.6611.56
51.20
ImGAGN [42]
92.89e0.45
83.52.051
60.53s1
94.55a1.
95.25a1.19
$3.11
49.98.074
54.92s1
GraphSMOTTE [70]
95.14-0.16
86.59
91.77-009
96.51-0.4
98.28-0.31
56.92-0.23
51.71+006
53.79-0.27
GraphENS [37]
96.32-0.3
87.46
93.26+0.11
97.70x0.00
98. 40.05
93. 03.04.000
58.54+2.1
52.33+0
16.10--.1
GraphMixup [60]
96.23.0.13
85.8660.30
93.81
98.2440.06
27.007
92.75.009
61 61.05
53.78 39
52.70s0.12
LTE4G [67]
95.67:033
142099
94,90s0.9
26.85
6920.25
63.31
53.8340
54.3620.4
[49]
96.74-0077
88.41
93.71sn07
97.69en.10
98. 98.71
93.07
58.71
51.17s1.18
55.72:0.7
TOPOAUC [8]
97.09-0.16
88.62-0.90
11,04-135 .22
93,96-1.6
65.86-0.52
53.47+0.4
54.78-035
GraphSHA [24]
96.27-005
87.36.0.2
93. 03.14.0.10
97. 97.7840.06
98.74-0.06
93.39.0.11
58.19.2.52
52.33+0
12
100 (High)
GCN (bh.) [21]
91.55-0.30
80.26.0.32
49
87.24-1.56
76.98-142
92.87-0.12
57.86-065
51.16.00s
50.79.0.79
DRGCN [48]
89 80.0.4
19.58
84. 69
92.09.0.75
96.5040.83
55.79e1 06
49.2440.9
54.87-015
DPGNN [57]
87.41.209
78.59.1.1
90.02s2.99
95.34a1.59
97.09a0.57
59.14.236
54.25.1.11
50.35an72
ImGAGN [42]
88.38s1.99
81.37
87.52s1.15
92.75a1.38
84.0772
52.73s2.44
49.44s07:
53.60s1.51
GraphSMOTE [70]
93.29.0.14
82,56
-8.88-1227 27
89.52-1.39
84.03-1.4 .44
56.82-0.5
51.49+a.1
52.51+231
GraphENS [37]
95.55-0.13
40.91
18.3840.1
97.74-0.06
98.665-0.0
92.8 0.0.
58.15+1.00 92
52.87.0.5
50.91+1.77
Grxph [60]
92.31-0:2
82,50+a
00.58.0.0
97.06=0.17
93. 85.0.99
92.03.009
58.73+0:27
53,2440.
52.4660.14
LTEAG [67)
92.82sn.56
83.87.1.13
90.77a291
97.19sat11
97.26a0.46
59.10sa..9
52.60s0.1
53.96an677
TAM [49]
96.24-004
87.22:a25
93.14:005
97.75.0.05
98.65
92. 02.84.0.mm 10
$6.81
42,99
52.42sn.14
TOPOAUC [8]
90.42-166 64
86.50
93. 14-0.6
61.71-0.30
52.17-028
53.31-0.34
GraphSHA [24]
95.73-0.11
85. 10
90.09.3.50
97.51-0.14
9% 08.62.00.6
18
56.00x2.91
52.87-0.55
50.72-0.8
36

---

Published as a conference paper at ICLR 2025
D.1.2 EFFECTIVENESS OF NODE-LEVEL LOCAL TOPOLOGY-IMBALANEE ALGORIHTS
Table D.5: Accuracy score (% + standard deviation) of node classification on manipulated local topology boglogy-imbblanced graph datasets with changing imbalance levels over 10 runs denotes out of memory or time limit. The best results are shown in bold and the runner-ups are underlined.
Algorithm
Cora
CiteSeer
PuhMed
Computers
Photo
ogbn-arXiv Chameleon
Squirrel 0.22
Actor 0.22
0.81
0.74
0.80
0.78
0.82
0.65
0.23
Imbalance Ratio: Low
GCN (bh.) [21]
80.16.097
66.99-1.7
83.97-0.14
70.39-1.68
87.28+2.77
55.45-006
50.42+1.2
30.87+060
24.23+1.24
DEMO-Net [59]
41.40.0:3
68.42s0.72
82. 62.70.
79.07
88. 88.0011.1
65. 1a.35
56. 182462
38. 18.864777
29. 39
meta veec [30]
38.11+1.36
24.77-2.30
59.93-1.95
71.13:041
37.16=033
33.61-0.5
41.45-046
25.98-a07 14.47
Tail-GNN [31]
80.162064
70.37a0.7
84.5620.30
86.40sa992
19
51.87a079
31.892195
28.672047
Cold Brew [72]
75. 75.3741.07
65.16
86, 1s
79. +0.40
85 24
68.50
58.78.0.19
39.57
32.93:0.5
LTE4G [67]
10
69.17aa.9
64.6420.30
81 $1.24:2.79
22.47
58.61an98
25.74
24.53a1.12
RawlsGCN [19]
29,95.0.2
72.20e0.5
s9
85, 15.97
78. 74.2.0
87.89+0.10
41. 31.70
44,91a115
29.684085
28. 28,5440.12
GraphPatcher [17]
84.00-0.2
85.58-0.13
87.60-n.23
93.20-0.22
66.35.0.00
55.77+104
35.16+022
27.15-030
Imbalance Ratio: Mid
GCN (bh.) [21]
80.16.1.09
66.87-085
83,97-0.13
71.65+2.10
89,43+0.55
52.93-0.33
52.74.0
28.70+0
21.55+1.24
DEMO-Net [59]
80,37
69.73s1.31
84.11
79.38s0.98
88. 13.0991..0 1.30
65.81
55,51
39.45+062
29.12:0:30
teta-tail2vve [30]
32. 32.17.0.8
29.97-361
59.82-1.86
68.17711.0
79.82+1 02
33.71+1.16
38.78-0.44
24.90+0
26.099.007
Tail-GNN [31]
79,05a1.15
69.97s1.01
85.78a041
84.0921.01
92.21
53.20a030
30.43+1
28.02:0.1
Cold Brew [72]
13
67.42-0.97
86.51-0004
80. 10.094
88. 13-22
69.97-0.0
59.16-044
43.004-024
33.01.0.9
LTE4G [67]
82.54aa.s
70.55a0.4
84.77a075
81.32+2.21
91.09
55.8442.6
32.4343.31
24.00sa.49
RawlsGCN [19]
80.52a014
42.38
86.05=0.12
78.78+1.40
90.53+1.32
40.00
44, 44.962079
29.93+9.6
28, 29:029
GraphPatcher [17]
83.25a0.42
73.38.0.42
35.60ao.16
63.6820009
92.28
66. 66.7440.4
55. 19..41
36.94an.11
23.85x0092
Imbalance Ratio: High
GCN (bb.) [21]
78. 78.70 65.07a081
83,87a0.2
68.15
89.42s1 24
50.72.n.30
53.33x1.09
29.56x2.72
23. 23.86:
DEMO-Net [59]
78.23 62.14
83.51
78.34
88.08
65.76a0.18
54.08+141
36.98s1
28. 28.96:0.30
meta-tail2vee [30]
38, 16
21 31.62.1.70
58.39.2.25
71 71.0332.:0
66.37+2.96
35.31
37.94.052
28.18
25 35.98.00s
Tail-GNN [31]
81,20
69.6920.55
84,9520.7
86.39.0.82
53. 53.00a0.9
31.081091
28, 18.36
Cold Brew [72]
75.44+2.31
66.12.0.7
86.44-0..2
78.59.0.10 10
86.83+
70.32.0:0
59.47:0
40.1640
33.44:032
LTE4G [67]
81.93s1.43
67.09
84.30s0.49
83.33s1.99
92.12shh32
$6.39x2.9
30. 30.16s4.0
23.83:na5
RawkGGN [19]
11.66+0.17
69.88-0.74
74
75.72.0.77
79.27-041
87.99.1.16
39.14-0.16 16
42.22.0:17
28.5440779
29. 19.301-012
GraphPatcher (17)
80.77a023
43.13.0.45
85,74.0.14
85.4720.16
93.57
67.38a0:06
56.74.0
12.12a0
25.48:0.49
Table D.6: Balanced Accuracy score (% + standard deviation) of node classification on manipulated local appoogy-imbalanee graph datasets with changing imbalance levels over 10 runs. "_" denotes out of memory or time limit. Best results are shown in bold and the runner-ups are underlined.
Cora 0.81
CiteSeer
PubMed
Computers
Photo
ogbn-arXiv Chameleon Squirrel
Actor
Algorithm
0.74
0.80
0.78
0.82
0.65
0.23
0.22
0.22
Imbalance Ratio: Low
GCN (bb.) [21]
19,090
63.72.2.1
24.31
77.82 77.82+1.32
86.91
22.36an.15
50.82:039
30.8610
23.02a1.14
DEMO Net [59]
82.53+035
65.58-071
83.84-0.8
84.87-0.25
90.06-082
41.57~1.30
56. 18:045
38.85+078
26.59-a61
meta-tuil2vee [30]
27.64s1.24
19.99.1.0
73.78
55.6844.66
$0.39+0.35
4,46
40.58:0.2
24.4610
20. 15
Tail-GNN [31]
20
66.78=030
85.42.0.41
90.80-9.53
93,57=0.22
$1.96:199
31.89
38
Cold Brew [72]
77.412002
62.25a1.02
86. laaous
85.5820.35
88. 18.6721.18
47.29
58.05e0.20
39.562n119
29.01:1.40
LTE4G [67]
82
42.6840.43
67.45sa.40
85.15
87.35=2.33
92. 26.864444
58.15
25.73x2.58
24.31sn62
RawlsGCN [19]
21.80
68.80.0.7
16.76.
84.6720.64
90.592031
13.32a0.08
45. 15g15
29.692035
28. 13s0112
GraphPatcher [17]
84.66.047
68, 18.56.0.16
85, 25.6889.19 19
90.73e0.18
93.61:026
43.9 43.9770.00
58.28.102
35. 35
22,46x0.46
Imbalance Ratio: Mid
GCN (bb.) [2]]
31.5490.39
63.00za8:
84.4620.13
78.91
89. 58
1220.38
51.742005
28.6940
21.25:0:3
DEMO-Net [59]
81.75a0.5
65.52.1.00
84.99.0.u
86.24220.3
89.43
42.88a0.4
55.37a1.14
39.45a062
26. 70
meta-tuil2vec [30]
32.56,0.9
27.17
36.192
55. 60
81. 11.2621.76 78
68
39,92a0.22
24.91
20.08:0077
Tail-GNNN [31]
81.47+0.77
66.05-065
86.64-0.30
90.066-0.8
93.08-0.19
53.40-031
30.44.106
26, 26.26-033
Cold Brew [72]
76.00s1.85
62,88
26.41
85 6240.00
89.20s1 a5
47.73a0.13 13
58.71.0.4
43,04:025
30.65:019
ITE4G [67]
82.79.032
65.79.ast
85.07-007
87. $7.16+1.99 1.9
92.38-0.17
55.04+2.9
32,43+3.22
24. 14
RawlsGCN [19]
12.1
67.74.026
86.89.0.16
84.7621.49
91.50=120
11.6220.13
44.42+1.19
29.93an65
27.29:a:00
GraphPatcher [17]
83,94.0
69.17.0.2 22
85.72.0.0s
90.95:0.21
93,21
38.492041
54,39a0.1
36.93s0.11
23. 10:056
Imbalance Ratio: High
GCN (bh.) [21]
81.68-084
62.76.0.0
84.70+o.07
78.1559.40
19-19-0.3
15.93-0.27
52,93+1 49
29.54.2.72
22.83 22.83+0.57
DEMO-Net [59]
82.14
64.16.8.6
84.70s0.9
87.19s0.50
90.51
22.00
14.11a1.0
36.37x1
27.16:2.28
meto-tuil2vee [30]
25, 234734
17.49a1.12
52.61a2.40
67.44.2..57
72.792867
1.82
36,662065
25.20
20.03:005
Tail-GNN [31]
83.79a0.4
67.15a0.1
86.0720.1
90.72.0.50
94.62=1:22
53. 12anc9
31.09a191
27.36za70
Cold Brew [72]
78.25a1.72
63.45a1.10
86.432000
85.73e0.10
14
48.43a0.16
59.664017
40.1620116
30.68:018
LTB4G [67]
84.15+1 36
64.63-065
85.12.0.3
89.78-0.59
94, 24
26.25.308
30.15 10
24.03+0.5
RawlsGCN [19]
83.192022
67.514041
86.60...10
86.25.a.13
91.82=024
10.65
42.87sna1
28.54a0.79
28. 14
GraphhPachher [17]
83,91+0.11
68.89-am
85.78-0.18
91.23+0.05
93.57+a.13
40.59+0.39
76.78-035
37.1140118
23.98-032
37

---

Published as a conference paper at ICLR 2025
Table D.7: Macro-F1 score (% standard deviation) of node classification on manipulated local apooloy-imbbllnneer graph datasets with changing imbalance levels over 10 runs. " denotes out of memory or time limit. The best results are shown in bold and the runner-ups are underlined.
Cora 0.81
CiteSeer
PubMed
Computers
Photo
ogbu-arXiv Chameleon
Squirrel 0.22
Actor 0.22
Algorithm
0.74
0.80
0.78
0.82
0.65
0.23
Imbalance Ratio: Low
GCN (bb.) [21]
77.96
63.07a1.7
82, 18
58. 58.70s2.08
82,92+233
21 11.64
50.63+1.22
19
19.05+277
DEMO-NG Net [59]
79,01=0:52
64.74.0.7
81.93=0.2
65.66+1.00
84.73+1.70
43.08=1.0l
55.67:0.53
38.58:0.2
26.45-0.72
meta-tail2vee [30]
23.87a1.9
11.60x2.38
53.82a1.49
50.14
71.662931
6.68
40.1
22.06x1.32
9.48s1.49
Tail-GNN [31]
77.91=0.37
66.32s045
84.05a0.0
75.59
89.56.a.35
51.09:a30
29.90sh.46
26. 26.95-n65
Cold Brew [72]
73.42a0:3
61.70
85.41
65.7
81
48.39
58.50
38,90
26.8 26.89:1.9
LTE4G [67]
59,4940.5
66.21:0.6
33,6440.33
69.5113348
89,78
58. 48,
24.48
23. 25.15
RawlsGCN [19]
77.88-028
68,20+0.0
15.43-0.12
67.01+2.37
85.49-0.34
14.56+0.05
43.80+1.19
29.24x0.50
26, 26.80+a.10
GraphPatcher [17]
81.644075
28
84.65.0.18
78.27:0.00
90.48:0:46
44. 04
55.67a098
35.11
19.03:095
Imbalance Ratio: Mid
GCN (bb.) [21]
78.43
62.70.a.1
82,81
60.4332.55
84,99
17. 17.40s0.42
12.11
27.48+1.74
19.37
DEMO-Net [59]
78.11.054
65.23+1.
83.44-0.00
67.75-0.71
14.14-1
44.63-0.9 59
55.177098
38,93+066
26.48-0 39
meta-tail2vee [30]
30.58s1.61
19.16:3.25
54.8620.6
49.59s1.24
86.33=182
6.62e0.98
38.29sh62
24.30
8.70a042
Tail-GNN [31]
77.40+1.05
65.77-081
85.23-044
73.31-1.40
83.73-013
52,53+074
27.98+0.9
25.68-061
Cold Brew [72)
71.85+2.17
62.70:1.00
85. 85.69
66.03an.20
84.2621116
49.82a0.18
58.91
42.07am.40
30.71:0:0
LTE4G [67]
80 80,29
65.76
83.662088
68. 68.6553338
87.57
55,32+295
32.20a3.71
22.78+0.50
RawlsGCN [19]
78 28.30ao.25
67.50
85 19
66. 62-2.0
87.77z1.45
12.56a0.20
44,442111
29.48a
26,32:021
GraphPatcher [17]
40.92.0.2
28.95.0
84.6 84.6520.1
74.74
88
40.76
54.7240.3
37.0640.11
22.28:0:58
Imbalance Ratio: High
GCN (bb.) [21]
77.03a1.19
11.898066
82.72a0.32
58.78a4.61
85.73
14.52a0.27
52.56x1
27.43
20.48:2.59
DEMO-Net [59]
16.85+1.11
63.38:0.8
82.87.0.3
65.92:0.82
84, 84.70.023
43.74a1.0 02
53.73a115
35,94+1 44
27:24:028
meta-tuil2vee [30]
21.82a1.45
7.56G233
52.0323.18
54.07a2.19
65.2227.60
1.7
34.06s122
23.00+000
8.30
Tail-GNN [31]
79.6640
66.29.0.3
84.31
75.04+1.16
89.67-0.39
62.67:0
28.08+1
25.85+035
Cold Brew [72]
73.71=207
62.71s076
85,72.0.2
65.83.0.13
83.37
50.43
59.18:023
39.43an411
20.32:0.8
LTT4G [67]
80.57-1
63.70-0.66
83.11+0.54
73.38-1.68
89, 18-058
55.92+2.00
28
22.95-061
RawlsGCN [19]
19,19
66.41a0.5
11.0u
69.00sa.95
85.7921.10
11.24
41.86
27.86
27.41s0:16
GraphPatcher [17]
79.35a0:15 68.6920.00
84.7420.16
77.10
90,94
42.93a0.9
56.05e0.29
17.34
20.10:
Table D.8: AUC-ROC score (% + standard deviation) of node classification manipulated local aypology-imbalanced graph datasets with changing imbalance levels over 10 runs. " denotes out of memory or time limit. The best results are shown in bold and the runner-ups underlined.
Algorithm
Cora
CiteSeer
PubMed
Computers
Photo
ogbn-arXiv
Chameleon Squirrel
Actor 0.22
0.81
0.74
0.80
0.78
0.82
0.65
0.23
0.22
Imbalance Ratio: Low
GCN (bb.) [21]]
96.34s051
87.80
94.8920.06
95.61
97.82
87. 8.24.00
78. 78.762027
62.68
53.43 53.43,1142
DEMO-Net [59]
13
88.66:0.0
94.22-0.07
96.52-0.10
98 29:00.
92. 39
:0.31:034
68.00
35.96:033
tela-tail2vee [30]
62.83s1.22
53.44-2.0
71.50a3.86
89.26s0.64
94, 15
62.42-256
69.63.a28
53.44mn22
50,50+a35
Tail-GNN [31]
96.55+005
89.114056
94.28-0.60
97.92-0.11
98. 10
76.06
63.9141
59.72+0
Cold Brew [72]
93.87a0.5
87.38=0.9
95.6720.13
97.88sn.05
98.71
78.37an
66.72an
65.12:105
LTE4G [67]
96. 142..7
88,78a1.08
94.5220.45
92. 02.94=2.66
98. 83
78. 18.00s1.55
58.28
56. 172026
RawlsGNN [19]
84
95
96.34-..m
97. .7..07.0.0
98.99.002
79.78+0.1 12
71. 71.94.009
58 88.8
59.3410.1
GraphPatcher [17]
97.10.0.:
90.75.0.15
94, 98.08
97.8820.05
98.5420005
90.9020:00
79.09a0
66.652030
53.80
Imbalance Ratio: Mid
GCN (bb.) [21]
95. 25.8880.29
87.55.0.33
95.0 95.0720.66
95.70
98. 08.05
86.5520029
78. 28.60ga33
62.45an74
51,23s0.46
DEMO-Net [59]
05
88.31
94..85
97.14.0.18
97. 13.75
29
a0.3
67,9610
59,540 49.5440.5
meta-tuil2vee [30]
65. 65.8840.9
59.3920.47
73.30g1.00
90.4520.24
94.662964
64.91a1.30
68.34g042
53,852004
49,4 20
Tail-GNN [31]
96. 19
89.73:0.39
95. 17
97. 19.98...1
98. 27
76.40:0.4
62.60s137
58. 144611
Cold Brew [72]
93.14
88.06=1.14
96.06=
98. 98.03:0.00
98 33
95.66-0.66
77.61+013
68.96
65.47:a.17
LTE4G [67]
95.
89.6920.4
94.41
93.05s2.75
97.742033
77.8021.3
61.90x144
55,0820.8
RawlsGCN [19]
96.65=007
91.5 43
96. 29.004
97. 97.533mn00
98.97-n02
79.8 22
71.42+a15
59.10+008
59.19.a.4
GraphPatcher [17]
96.66.005
91.74.0.09
94.63a0mz
98.05
04.142002
92.04a0.11
78.362026
66.40an.12
54.642062
Imbalance Ratio: High
GCN (bb.) [21]
96.12s0.3
87.93u0.s
94.96so.us
95.422a0.9
87.28s2.77
84.44.000
78.63en33
63.00x136
53.72sn.0
DEMO-Net [59]
95.
19
87 64.44.00
94, 22.0s
17.102
98. 15
93.45
79.19am39
66.28+1 10
58. 89:0.8
meta-tail2vee [30]
61.19a1.02
49.89s1.49
69.63a1.44
92.90sa.31
91.77=2.16
62.67a1.1
68.624a77
55.24
50.0420.4
Tail-GNN [3]]
96.80so.5
89.96.0.2
95. 10
97.93.0.10
98. 18.60
76.81
64.39H042
59.60+106
Cold Brew [72]
94.044004
88.26-0.97
95, 05.90
97.82 07.82-0.05
98.87-0.10
95.86-0.06
78.97-034
67.7240
65.52.0
LTE4G [67]
96.17.
86,40z2.05
94.4620.31
95. 95.9721.48
98.722006
77.34
60,35a265
54,98:034
RawlsGCN [19]
96.87-oms
90.42-0.11
96. 16-06
97.51-0.44
99,21
79.47-6.15
71.04-a11
58.32+012
59.38-a.1
GraphPatcher [17]
15.15
91.55aa.ss
94.90so.2
97.59um.05
98.75
92.53am.05
78.67am15
65.82x0.40
56.032a119
38

---

Published as a conference paper at ICLR 2025
D.1.3 EFFECTIVENESS OF NODE-LEVEL GLOBAL TOPOLOGY-IBBALANCED IMBALANCED ALGORIHTS
Table D.9: Accuracy score (% + standard deviation) of node classification manipulated global aapllog-iibbllncee graph datasets with changing imbalance levels over 10 runs. " denotes out of memory or time limit. The best results are shown in bold and the runner-ups underlined.
Cora
CiteSeer
PubMed
Computers
Photo
ogbn-arXiv
Chameleon Squirrel 0.23
Actor
Algorithm
0.81
0.74
0.80
0.78
0.82
0.65
0.22
0.22
Imbalance Ratio: Low
GCN (bb.) [21)
81.09
70.39
84.44m1.20
76.23
16=1.6
33.09Hn.12
37.80sn.59
25.15
24.34+0.8
ReNode
81 31.94.0.45
71.93
83.86an.13
79.42at.70
89.91
52.75an.14
37.67a0.
25.36.0.49
24.65.025
TAM [49]
81 38,0800.3
74,06.0.2
84.26.0.8
84,17=0.18
91.93-0.22
54.16.006
38.78s0.17
25.64.0.12
24.774033
PASTEL [52]
82.49-0.4
74.38-a31
85.08-n.84
91.22-0.40
54.05-1.3
34.01-0.57
29.50-0
TOPOAUC [8]
81.3% 81.3800.0
72.31
77.23a1.
89.0 89.04-0.96
68
23.52=0.78
25.88+097
Hyper[MBA [12)
80.67:0.64
73.46x070
85.1 16
85.22.0.64
92.75-0.11
43.48s1.30
32.69:0.06
27.09
Imbalance Ratio: High
GCN (bb.) [21]
79.10s1.25
68.3741.75
83.44201.16
75.02a2.00
86.32.1.90
51.04a0.18
33.90s0.70
23.27=0:22
22.40z0.68
ReNode [7]
79.91
69.89.073
82.9740.12
77.95a1:71
80.0.5
50 15
32.92s0.88
23.80.0.59
22.39:002
TAM [49]
80.50ga.18
73.14g015
84.07e0.12
82. 82.35
89 80
52.09
35.6420227
24.58:0.09
22.55e000
PASTEL [52]
80.91.0.66
72.73.0.6
83.24.0.85
89. 10:0.41
47.12x282
33.15-0.66
27.56:106 04
TOPOAUC [8]
79,27=0.3
70.08eax3
75.35a1.32
87. 17.10
33.39:2.09
22.86.0.36
22.56e0.18
HyperIMBA [12]
79.81
71.78a0.00
84.75a0.30
83.43
90.65-0.14
38.30s2.70
29.97a1.79
25.30a2.50
Table D010: Balanced Accuracy score (% + standard deviation) of node classification on manipulated
global -inaagyyd graph datasets with changing imbalance levels over 10 runs. denotes out of memory or time limit. Best results shown in bold and the runner-ups are underlined.
Algorithm
Cora 0.81
CiteSeer
PubMed
Computers
Photo
ogbu-arXiv
Chameleon Squirrel 0.22
Actor
0.74
0.80
0.78
0.82
0.65
0.23
0.22
Imbalance Ratio: Low
GCN (bb) [21]
82.78.0.52
67.45x081
85. 17
85.09.1.3
89.28s1.00
26.76.0.20
38.28.0.50
25. 25.14
23.78
ReNode [7]
82.89
68.52a1.14
84.52a0.11
86.9320:3
90.03.051
36. 36.79
38.02a0.10
25 29.3620.99
24.04
TAM [49]
82.49=011
70,97s013
84.71a006
91.810113 89.91
39.96
39.16a1:14
25.63en.12
24.25an11
PASTEL [52]
83,462032
71.172028
90.4 10.3
93.56.0.11
$4.27a1.18
34.0220.7
26. 894043
TOPOAUC [8]
83. 83.15
68.074021
76.90+4 12
87.93
38. 1640.6
23.51
23 36:03
HyperlMBA [12]
82.32.041
70.75a0.56
86.45
91.54.0.30
12.36
43. 43.39.1.43
32
28.4553.45
Imbalance Rutio: High
GCN (bb.) [21]
81.99.0.1
64.6620.91
84. 22..12
83.42a1.65
87.36s1.02
34. 34.78.0.21
34.75am.77
23.27an:2
22.52:0.42
ReNode [7]
82, 71
66.04:0.22
83. 852009
85 43,0.48
88. 10
34. 19
33.87
23.80
22. 67:3373
TAM [49]
82.87
69.8120.11
84. 594008
87.88.0.09
89.7020.14
37.92.0.6 =
36.184025
24.58an09
23.15
PASTEL [52]
83,36.0
69,71
88, 92,9920.39
91.40-0.12
47.41:227
33.15
25.55:057
TOPOAUC [8]
82.28.0.3
65.82+1.20
74.75
86.00=a.5
34.45+1.56
22.85+n.36
23.27:026
HyperIMBA [12]
82.5440
68.9740.38
85.64.0.2
89.74:031
90.25s0.17
38.00s3.16
29.96+1.29
26.77:2445
Table D.I:: Macro-F1 score (% + standard deviation) of node classification on manipulated global graph datasets with changing imbalance levels over 10 runs. denotes out of memory or time limit. The best results are shown in bold and the runner-ups are underlined.
Algorithm
Cora 0.81
CiteSeer
PubMed
Computers
Photo
ogbn-arXiv
Chameleon Squirrel
Actor
0.74
0.80
0.78
0.82
0.65
0.23
0.22
0.22
Imbalance Ratio: Low
GCN (bb.) [21]
79.45-073
66.81s104
83.54-0.19
64,78=2.00
84.12-144
33
36.69ens5
24.85-0.65
23.13
ReNode [7]
80.26.038
68.21gam1
82.98an.12
68.612147
86. 1420.6
33.88
36.60.1.50
24.75=0.1
23
TAM [49]
79.01
70.30ga13
83.22an.08
75.36
88. 28.322..22
36.75
36.45s0.19
23.59.a.27
23.44:020
PASTHL [52]
80.79-0.5
70.62-032
73.94+1.06
88.17-0.4
53.30-1330
33.54-0.60
26.34-023
TOPOAUC [8]
79.75
68.01a1.03
13.3.3
84.39s4.10
36.76.101
21.50aa.71
22.76:a70
MyperIMBA [12]
78.85-066
69.96-a.5
84.16-0.6
73.55-0.72 72
89.45-0.21
42.83+144
30.26-1.87
26.41+317
Imbalance Ratio: High
GCN (bb.) [21]
78.12.1.02
64.20a1.32
22.55
63. 63.5442..5
82.92a1.50
31.85a122
32.39
22.3621.02
21.6620.5
ReNode
78.80
65.50g069
82.08
42.122
84,20
31. 11
30.82+1.11
22.77=1.09
21. 11.69
TAM [49]
79.34-021
69.13-a11
83.17-0.1
73.25-6.3
86. 26.25-0.21
34.68-006
33.95.0.38
22.52-o.17
22, 10-000
PASTEL [52]
79.37
68.994028
72.45at.0
86.25.0.4
46.5913.16
31.95-1.06
TOPOAUC [8]
78.24-0.4
65.48-105
58.54-3.54
82.50-4.15
29.95.3.52
21 21.06=1.40
15
HyperMMBA [12]
78.4420.99
68.2440.00
83.83
71.87
87.40...22
37.25
28.82=2.13
24.45a244
39

---

Published as a conference paper at ICLR 2025
Table D.12: AUC-ROC score (% standard deviation) of node classification on manipulated global poolooy-imbalaneee graph datasets with changing imbalance levels over 10 runs. " denotes out of memory or time limit. The best results are shown bold and the runner-ups are underlined.
Cora 0.81
CiteSeer
PubMed
Computers
Photo
ogbn-arXiv
Chameleon
Squirrel 0.22
Actor 0.22
Algorithm
0.74
0.80
0.78
0.82
0.65
0.23
Imbalance Ratio: Low
GCN (bb.) [21]
94,82s0.2
88. 18.443113
14.111
94.98at.1
93.61=1.77
88 38.4911114
66.27am187
54, 34,98.0.99
54,74a022
ReNode [7]
95.16
88.41a099
94.06s0.00
94.91s1.26
93.97.1.80
18.42:0.16
66.08s9.00
55.21
54.83+020
TAM [49]
96.75-0.4
91.87.007
94.86.0.01
98.1 98.177
99.01-0.01
92.30-000
65.00+0.37
55.10+0.10
55,444024
PASTEL [52]
97.05-our
92,90.a11
98.45
29.28mm.
80.43:0.46
63.47:0.47
59.43+030
TOPOAUC [8]
97.07
90.67a067
62.28
98.54
74
52.72.0.54
55.2
HyperIMBA [12]
96.19 19
91.50e051
a5.31
98. 39.0.06
98.71=0.08
28.4882.04
60.29s1.4
59.92:331
Imbalance Ratio: High
GCN (bb.) [21]
94.97a057
87.95
93.02a0.17
93.05st.22
91 15
86,4330.15
62.31
53.67=0.33
53, 730.99
ReNode [7]
95.00+0.5
87
93.23+0.21
93.75-1.27
92. 15-1.
86.42-a017
61.68-1.15
54.15-0.49
53.02-0.18
TAM [49]
96.78so11
92.04a012
96.23
97.20=6.0
90.25
62.91am62
54.27=0.6
53.49:a06
PASTEL [52]
97.31
92.65a0100
96.75
97. 10.000
76.49
63.78.0.40
57.70
TOPOAUC [8]
96.54a02
89.88aa25
90.892243
96.40za.15
60.37a1.22
52.77=021
53,962a21
HyperLMBA
96.57a030
92.23g0.2
94.95a0.13
96.85a0:07
96.5520.1
64.57s144
58.83-2.08
57.20+258
40

---

Published as a conference paper at ICLR 2025
1.1.4 EFFECTIVENESS GRAPH-LEVEL PLASS-IMBALANE ALGORITTMS
Table D.13: Accuracy score (% standard deviation) of graph classification manipulated class- imbalanced graph datasets with changing imbalance levels over runs. " denotes out of memory time limit. The best results shown in bold and the runner-ups underlined.
Algorithm
PTC-MR FRANKENSTEIN PROTEINS
D&D
IMDB-B REDDIT-B ogbg-molhiv COLLAB
(Balanced)
GIN (bb.) [63]
50.43+266
64,2742.47
65.3442.2
64.04a3.79
66.05-2.57
76.661488
65.31
G'GNN [58]
83.70
63.63s1.16
63.30
66.07a1.27
61.91
72.34:276
53.8242.2 26
Topolmh [
10.91
61.45+374
55.04.513
66.57-181
66.28-135
73.99-1.18
65.92+1
DataDec [68]
54,0544
66,90s336
65.24:4.05
64,46s1.88
64.09
79.29s8.1 18
72.24
ImGKB [54]
53.48+3.50
52.54x605
69.85-1995
65.45-288
50.16+0.34
50.24+0.99
39.34x10.8
P
20 (Low)
(bh.) [63]
47.83x2.95
63.38+1.9
55.38
51.05a5
62.31.3.99
61.10:488
60.75
65.01+1.3
G'GNN [58]
51,8846
61.13+1.05
63
36.2997.30
63.8 63.87
69.58+3359
65 65.00s5.81
62.05a3.05
Topolmh [71]
44.86x3.52
49.49.7.1 14
52.12+
49.97-1.24
59.95-5.9
59.6747.30
65.88+0.75
DataDec [68]
88.72x288
67.99.075
66.58
63.5141
67.92-337
78
71.48:100
ImGKB [54]
50.1145.5
40.83en02
66.60.2.4
65.85-1.70
47.74x0.20
48.57x2.14
67.50-2.70
51,21
100 (High)
GIN (bh.) [63]
39.42.187
56.02+1.45
42.50)+205
51.5446.57
53.57-331
55.564785
62.000.308
GNGNN [58]
96.52:999
55,414391
52.97a13.44
55.38415.00
59 49
63.22s467
62.61
Topolmh [71]
39.42.1.24
46.45+6.77
39,23+4.28
39.12-1.62
47.75-3.73
64.19+1.27
DataDec [68]
58.69a3.10
67.82s188
61.99.711
65.77
66.34-66.0
77.72s5.12
71.50
ImGKB [54]
44,24.565
38.34x001
61.46x10.25
59.99:7.57
47.08:3.72
51.25x5.10
50.20+006
Table D.14: Balanced Accuracy (% + standard deviation) of graph classification manipu- lated class-imbalanced graph datasets with changing imbalance levels over 10 runs. " denotes of memory time limit. The best results shown in bold and the runner-ups underlined.
Algorithm
PTC-RR FRANKENSTEIN PROTEINS
D&D
IMDB-B REDDIT-B oghg-molhiv COLLAB
(Balanced)
GIN (bb.) [63]
61.40a164
64.33
64.90
63.37a326
66.05x2.57
76.6644.8
72.9921.33
GPGNN [58]
53.42x3.2
63.55:t.22
64.39.221
63.79x211
61.914377
72.34
67.17.
TopoImb [7]]
53.9942.19
60.81=283
59.7
67.19s2.6
66.282135
73.99a1
51.93x2.5
DataDez
53,70
65.06.5.25
62.39x238
62.96e1.21
64.224573
79.802738
62.31
ImGKB [54]
53,344561
49.98-0.0
68.09-2.49
62.33
49.99
50,24+0.29
33.38-0..0
20 (Low)
GIN (bb.) [63]
51.36x2.25
61 90
60.399.202
57.33=0.16
63,5445.46
62.89
60.75.3.79
47.03 445
G'GNN [58]
52.75x2.14
63.31=1.14
66.18.3306
61.09a4.11
64.28.5.2
70.26
65.00
60. 70.26.2.04
TopoImb [71]
50.4423.75
56.57.3.30
59.88a6.15
58.332140
64.14
61.34a6.80
48. 48.95a1.4
DataDee [68]
53.42:235
66.10.1.2
61.54x2.35
61.27a1.04
67.95x2m7
78.68
68.71=1.11
ImGKB [54]
51.6143.2
50.01
64.7245
63.39
50,23g028
50.0740.15
67.50
33.3320.00
p
(High)
GIN (bb.) [63]
47.89x212
54.66-1.51
52.47-4.58
57.46x2.7
59.54+7.11
44.67-2.88
G.GNN [58]
50.76a1.78
60.38.1.91
51.3246.16
53.17a2.00
61 35.555533
65.974400
54.91
Topolmb [71]
49.99ea.3
$5.82-4.93
53,96.278
$2.05s1.31
$2.8243.06
55.874400
47.98:1.6
DataDec [68]
55.224581
65.24.2.16
60.2243:13
61.6022.00
66.3021.5
77.7745.9
68.99.2.04
ImGKB [54]
51,3843.53
50.00s0.01
64.48s5.90
59. 59.14
50.07:0.3
50.28ah23
33.33s0.00
41

---

Published as a conference paper at ICLR 2025
Table D.15: Macro-F1 score (% + standard deviation) of graph classification manipulated class- imbalanced graph datasets with changing imbalance levels over runs. " denotes out of memory time limit. The best results shown in bold and the runner-ups underlined.
Algorithm
PTC-MR FRANKENSTEIN PROTEINS
D&D
IMDB-B REDDIT-B oghg-molhiv COLLAB
(Balanced)
GIN (bh.) [63]
48.85-3.3
63.86-2.30
63.98-2.0
59.87-7.44
65.24-321
76, 50
60.83-161
GºGNN [58]
52.88.3:00
63.28et.13
63. 39.399
63.31a242
60.99:350
71.7448.14
46.71
Topolmh [71]
48.33-3770
53.13-572
65.85-2.29
73.41+001
51.32s4.69
DataDec [68]
52.98s4.5
63.6449226
22.20
62.83a1.20
62.42.8077
79.02s8.3
63.82:1.02
ImGKB [54]
50.36:5.9
34.59.2.65
67.98-243
61.06=7.66
35.27.474
33.97s042
18.66:343
p
20 (Low)
GIN (bh.) [63]
46.63-2.05
61.27-2.51
55.20+1.70
49.89-6.1
59.66-504
53.49.6.55
G'GNN [58]
47.644763
61.11e1.06
62,89.4.0
55.34a8.00
61.37,864
69.03+3.78
62. 02.39.6639
55.48-2.78
Topolmh [71]
40.26:2.06
43.64-11151
49.66x12.56
47.37=9.53
56.78:824
54.07e11.22
47.31
DataDec [68]
52.31
66.22a1.25
61.66a2.33
61.1224.22
67.42.3.0
77.9625.66
68.49.0.00
ImGKB [54]
44.624836
29.05a0:08
62.49ss.12
62.91
32.70a062
65.874331
65.87.381
22.58:0:00
p
100 (High)
GIN (bb.) [63] 35. 14.4.1
23.81
+1.20s2.65
38.83
47.51a5.47
18.74211.6
36.37a0.90
GCGNN [58]
37.35x7.10
54.73e4.33
44.16
42.22a11.30
$6.79.u227
61.15
50.73e4.11
Topolmb [71]
32.16:327
40.55a1032
34.48a661
34.24.2.00
36.642635
41,811990
45.32a0.00
DataDec [68]
54.762481
64.94u2.9
58.47s492
61.672267
64.8228.14
77.3925
68.8721.57
ImGKB [54]
41.355
27.73+0.44
59.75ar1:28
57.16s5.4
32.23s161
34.31s268
22.28.0.00
Table 1.16: AUC-ROC score (% + standard deviation) of graph classification manipulated iobaiiebalnneed graph datasets with changing imbalance levels over 10 runs. "_" denotes out of memory or time limit. The best results are shown in bold and the runner-ups are underlined.
Algorithm
PTC-MR FRANKENSTEIN PROTEINS
D&D
IMDB-B REDDIT-B ogbg-molhiv COLLAB
p (Balanced)
GIN (bb.) [63]
52.26x295
69 20.20.33
67.91
66.54
73.99,241
87.61
86.80e1.2
G:GNN [58]
54.5545.5
08.0331.39
67.094307
70.05a2.41
64.872148
80.22+401
79.90an.0
Topolmb [71]
56.93s4.9
69 19.011117
69,33:409
72.86e146
74.83.101
81.49:300
85. 12:0099
DataDec [68]
54.5746.2
72.65-1.55
68-8044316
68 18
72.25+565
81.26+1376
87.29-0.32
ImGKB [S4]
54.0945.28
54.78-2.66
73.47:2.00
66.54.2.05
50.60+1.2
74.3625.l
50.29
p
20 (Low)
GIN (bb.) [63]
51.28s4.16
24.222
59.21x3.70
54.13a6.72
74.38s2.4
84.08
76.76x2.18
86.05+1.11
GCGNN [58]
51.904385
68. 70...11
69.5943354
64.4923.43
69.0243.0
77.9724.2
72.074227
78.15.2.04
Topolmb [71]
90.82+3
67.96 27.96-2.26
66.774544
67.76
72.61
83.30
86.31
DataDee [68]
53.494195
73.98
69.32+181
67.05a1.47
75.40a3.25
81.00
85.68:2.32
ImGKB [54]
82.89:484
53.59-1.11
72.57+133
68.08-2.00
51.066+10s
76.25+3.00
75.76
50..42:091
p 100 (High)
GIN (bb.) [63]
47.04a3.22
64.26.4.79
59.00s2.00
47. 47.06=5.01
65.96.9.55
80,58
81.0423.44
G.GNN [58]
49.32x407
66.60=1.4s
52. 10.7.0
60.76
65.7947m0
72.55x564
75.67+1.51
TopoImb [7]]
48.0943.9
69. 48.4811.14
65.6243.19
61.925.30
69.12
80.08
82.28
DataDez
57.664555
73.51
64.35a6.6
69.11.287
74.89
82,59t6.0
87.03:121
ImGKB [54]
12,80+
54.03-2.17
71.98-2.56
63,79-404
51.044-157
71.65+6.88
50.05-0.9
42

---

Published as a conference paper at ICLR 2025
Table 1.17: Accuracy score (% standard deviation) of graph classification on manipulated class- imbalanced graph datasets with changing imbalance levels over 10 runs. denotes out of memory or time limit. The best results are shown bold and the runner-ups are underlined.
Algorithm
PTC-MR
FRANKENSTEIN PROTEINS
D&D
IMDB-B REDDIT-B
COLLAB
p (Balanced)
GCN (bh) [21]
48.62-1.12
52.67-6.11
65.44.273
63,97x4.02
59.76-1.76
66.65+1
61 33:32
GPGNN [58]
44.35-4.2
52.10<427
68.82-288
61,47.5.0
58.35e347
67 07.00222:55
49 39.4993.18
Topolmb [71]
50.61=4.99
48.03
57.414595
36.124461
49.52e1.01
58 18.6226.52
58.63 38.63e1..9
DataDec [68]
54,23-4.16
63.466-.36
67.25.895
63.10
58.20+406
69.08-4449
69.03-1
ImGKB [54]
52,83-5.45
23.97
64,57:9.12
64.93s4.64
50.155
50.299h.19
40.44a11.35
p= 20 (Low)
GCN (bb) [21]
48.59-9.57
58.32+1.51
39.06x2.17
53.81+1
GNNNN [58]
86.866
57.28e1
69.42:1.80
65.65a5
53. 11339
66 06.02:2.08
54.57a330
Topolmb [7]]
45 15.440
40.7
38 38.27:5.25
44.634482
49.75e481
54.35
$7.72+1.71
DataDec [68]
63.28-9.54
64,2337.24
64.6622.04
57.06.5.99
66.45-5.10
71.26+091
ImGKB [54]
49.49-5.12
40 40.822002
68.44+2.55
67.44:3.50
47.6550:25
48.58s2.15
51.21
100 (High)
GCN (bh,) [21]
40.58-7.61
43.03-9.39
37.34+3.3
42.48+2.61
45. 45.099...1
54.39x5.uk 16
50.47-0035
G2GNN [58]
41.78-2.81
49.50sa124
61,27:6.9
74
56.40e1.1
65 08.388
58. 58.0243:9
Topolmb [7]]
40.17
38.5020)35
33.21
36.50s1.44
18.3.00
52.21
61.40s2244
DataDec [68]
55.41-1.7
63.82-675
66.08-2251
65.07:2.40
58.58=5.07
65.56-8
70.48:00.0
ImGKB [54]
45.98
38.34ah02
65.09+281
58.21410.00
46.06.2.74
$1.23a5.0r
50.20s006
Table D.18: Balanced Accuracy (% + standard deviation) of graph classification manipu- lated class-imbalanced graph datasets with changing imbalance levels over 10 runs. denotes out of memory time limit. The best results shown in bold and the runner-ups underlined.
Algorithm
PTC-MR
FRANKENSTEIN PROTEINS
D&D
IMDB-B
REDDIT-B
COLLAB
p (Balanced)
GCN (bb.) [21]
50.07a023
50.00ea02
64..002.26
62.63x2.06
59.76e1.78
1666651..6
69.44-2.08
(PGNN [58]
50.02-006
51.82+181
67.39-1.6
60.38-583
58.35-147
67.02.2.55
61.96-0.00
TopoImb [71]
53.71
51.13x164
61.24a325
60.5622.30
49.71a034
58.68a6
44.78=3.2
DataDee [68]
54.3621.1
62.09
63.92a4.14
61.41:242
$8.19
69.08s1.3
12.11
ImGKB [54)
53.03
49.98s906
65.28a5536
62.84:2.56
50.15a
50.29e0.1
33.35s0.01
p 20 (Low)
GCN (bb.) [21]
49.66 19.69a0.88
50.73x2.05
$9.49ei.5e
60.53:1.45
$1.35at.88
63.51a3.57
37.97=2.15
(PGN [58]
49.73-087
53.76x2.15
68.31-1.72
65.61
53.84-133
66.54+200
61.19-1.4
TopoImb [71]
S1 6021.0
49.98am02
1422.22
54.87a2.95
48. 142444
56,51=284
46.73.087
DataDec [68]
14.50
59.94.3.7
61. 1..804.57
62.00..175
56.87
67.02.5
67.53-2.0
ImGKB [54]
51.70
49.99am02
67.46e1.22
63 70.3.6
50.14
50,08a0.16
33.34.0.01
100 (High)
GCN (bb.) [21]
50.36el.14
50,30en61
$1.78s1.94
$3.22:2.13
50.08a0.16
58.47s4.4
33,99
G2GNN [58]
49. 47
50.31
65.24-447
54.99+3.11
58.87-1.18
65.09+3.2
53.69-144
Topolmb [71]
50.7840.8
29.992002
50.01
49,47s1.20
01.0222:25
56.40s2.r
46.42:3.01
DataDee [68]
53,28-2.65
58.8743.26
63.07=533
60.83:261
58. 11:436
66.61+6.9
67.66-1.56
ImGKB [54]
50.19
49.992002
64.52e4.8
60.22s1.56
50.06an.31
50.26s0
33.33
43

---

Published as a conference paper at ICLR 2025
Table D.19: Macro-F1 score (% + standard deviation) of graph classification on manipulated class- imbalanced graph datasets with changing imbalance levels over 10 runs. "_" denotes out of memory or time limit. The best results are shown bold and the runner-ups are underlined.
Algorithu
PTC-MR
FRANKENSTEIN
PROTEINS
D&D
IMDB-B
REDDIT-B
COLLAB
p (Balanced)
GCN (bb.) [21]
32.8243.29
34.45
64.0842:4
02.02=2::
59,32s2.48
67.58s1.0s
36.55
G'GNN [58]
31.29a2.68
45,92
67.11a2266
56,99
56,4147.64
65.6343.26
41.15a415
Topolmb [71]
45.014836
37.18=706
56.62x6.1
55.05
33.04a044
50.17a12.11
40.73x3.26
DataDec [68]
23.24
6..26-4.55
64.05
61.3552.55
54.26+7.0
67.3746.0
62.14.1
ImGKB [54]
48 5348.31
35.15
62.33x11.50
62.3433.4
33.8420.00
33.97a0.41
18.9943.59
p 20 (Low)
GCN (bb,) [21]
31.49.5
53.81
58.06-144
36.70x6.28
57.56+6
GPGNN [58]
33.06s4.0
$1,9445.20
67.58+1/71
18.18-421
10.81
65.51
47.6 677.614889
Topolmb [?]]
39.66a977
28.9009.15
30,3647.82
40.50
37.79 58
45.50as
41.5991133
[68]
$7.35-6.49
60.8746.00
94
50.18-11.90
64.6246.8
67.94.1.4
ImGKB [54]
45.80
29. 29.04
66.63e1.90
63.41e4.10
32.52a0.48
32.82s1.2
22.58a000
100 (High)
GCN (bb.) [21]
29.74.6
31.00-6.00
32.66+5
40.59-3.18
31.21 40.
47. 47.46.8.8
35.27+2.66
GPGNN [58]
32. 03
34.5347.9
60.58s5.9
42.79-6.15
64.77a3.25
45 03.3335
Topolmb [7]]
32.03a3.31
27.74
24.89
31.9821.34
33.79a6.2
44 44.46st.15
42.6442376
DataDec [68]
52.48x3.00
56.32-7.38
62.2335.92
60.89u2.60
53.8748.7
62.46x13.54
67.68ab.4
ImGKB [54]
39.0848.03
27.76ah:0
61.1947.33
55.46e1144
31.73
34,27s2.64
22.28
Table D.20: AUC-ROC score (% standard deviation) of graph classification on manipulated class-imbalanced graph datasets with changing imbalance levels over 10 runs. denotes out of memory or time limit. The best results are shown in bold and runner-ups are underlined.
Algorithm
PTC-RR
FRANKENSTEIN PROTEINS
IMDB-B REDDIT-B
COLLAB
p (Balanced)
GCN (bb)) [21]
49,33x7.50
47.99s6.53
67.82x1.87
67.24a2.12
63,97a2.4
75.18
82.29.1.74
G'GNN [58]
45.4345m
53.96-1.95
70.27-246
68, 68.38.1189
61.49%6.19
74.01-3.6
76.39+1.0
Topolmb [71]
56.9844.1
57,57+1.0
69.62a668
70.29.1
18.800
77.48-1.a
74.54+1.3
DataDec [68]
75.99.4.75
69.51-3.35
69.52x3.0
66.85x3.20
62.53a3.42
66.49.9.00
27.38
ImGKB [54]
53.6145.87
54,93+184
72.75
67.82+1.8 10
72.90 72.98-5.05
49.9240.0
p 20 (Low)
GCN (bb.) [21]
45.8444.13
61.32a4.0
67.36s1.94
65.26x2.30
62.50e1.26
15.1192.08
81,28+1.6
(PNN [58]
48.93.5.15
54,45-3.6
71.85+1.86
71.00+1.85
57.06-474
73.96-2.66
76.39+1.06
TopoImb [71]
55.07a149
17.41
72.43a5.51
72.19.3.57
50.00a10.14
77. 77.58
77.08a0.50
DataDec 36.27:2.77
68.73-2.50
67.1847.60
16.1332..4
64.08-144
65.24-1134
87.01+0..
ImGKB [54]
52.91
54.52s2.20
71.1423.19
68.3422.86
51.08a071
26.70.3.52
100.94
100) (High)
GCN (bb.) [21]
44.65
66.38a5.0 76
65.59et.10
64.6741.0
56. 60.60.
76. 76.80s242
77.7742.3
G2NN [58]
46.8224.30
49.91
68.51
67.30+2.70
62.46e2.1
72.422379
70.8
Topolmb [71]
53.31a5.12
$6.71s0ma
70.74.4.14
57.78a6.66
52.4241028
77.07=0.24
75.9620.51
DataDec [68]
55.6841.33
68.13
69.26a8.47
67.68s1.9 96
63.17
64.92=1531
87.21
ImGKB [54]
51.0124.9
53.74a093
20.71at.2
65.42a3.01
$1.05a1.00
71.0125.58
50.01a0.s8
44

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Published as a conference paper at ICLR 2025
D.1.5 EFFECTIVENESS GRAPH-LEVEL TOPOLOGY- ALGORITTMS
Table D.21: Accuracy score (% standard deviation) of graph classification manipulated -malloggimbblanned graph datasets with changing imbalance levels over runs. " denotes out of memory time limit. The best results shown in bold.
Algorithm
PTC-MR FRANKENSTEIN PROTEINS
D&D
IMDE-B REDDIT-B oghg-molhiv COLLAB
Imbalance Ratio: Low
GIN (bb.) [63]
52.17a436
54 962100
63 63.58
65.01=0.9
66,38:427
67.41=2.22
59.35
64.34
SOLT-GNN [32]
47.544433
59.98-1.11
68.561183
63.78.1.06
64.20:4446
49.57
61.79.2.0
Topolmb [71] 49.71a199
53.13
61.19
65.16
66.00:241
69.47.3.70
62.71a242
Imbalance Ratio: Mid
GIN (bb.) [63]
51.38a678
24,82-2.26
62. 04.14
61.46=2.43
65.08
68.32s1.77
57.67a312
65.8423.12
SOLT-GNNN [32]
53104-391
68.71-1.00
71.95+2.6
63.33-1.86
69.38-122
73.51-1.14
69.69-245
TopoImb [71] 51.59a4.0
54.52a0.87
64,03s443
65,99-1.25
68. 10sas7
71.54,0.75
68.68a1.54
Imbalance Ratio: High
GIN (bb.) [63]
48.41a707
53.9927.96
58.00s419
60.68
62,60
67. 07.41=2.3
56.69.237
67.05=2.46
SOLT-GNN [32]
51.744525
67.88-2.97
72.04.2.18
64.97-324
65.03
60.24-2.11
67.12
Topolmb [71] 51.962115
56.32a0.1
54.89213.58
64.162296
66.75s091
69.14
67.52a0.7
Table D.22: Balanced Accuracy (% standard deviation) of graph classification nipulated topology-imbalanced graph datasets with changing imbalance levels over 10 runs. denotes out of memory or time limit. The best results are shown in bold.
Algorithm
PTC-MR FRANKENSTEIN PROTEINS
D&D
IMDB-B REDDIT-B ogbg-molhiv COLLAB
Imbalance Ratio: Low
GIN (bb.) [63]
51.08-207
55.22-1.3
59.76-1.78
63.46-0.22
66.38-4227
67.41-2.22
58.63+2.23
64.73+542
SOLT-GNN [32)
15.47a210
63.58.0.32
66.60.325
62.58:0.5
64.20a556
49.57s4.8
70.23a1.56
Topolmb [71]
50.07+277
54.44-0.4
63.87+166
67.24-1.5
66.00+241
69.47-370
71.56-1.66
Imbalance Ratio: Mid
GIN (bb.) [63] 49.83+1 30
54,43-2.04
56.84.2.4
62,22-0.98
65.0845.28
68.32-1.77
56.85.3.10
74.40+1.72
SOLT-GNN [32]
50.06ea75
69.3620.87
70.88
59.61=340
69.38:125
73.51st.14
75.86.1.12
Topalmb [71] 50.88
54.60+1.00
59.45
65.25-2.49
68. 10+087
71.54-0.75
76.54
Imbalance Ratio: High
GIN (bb.) [63]
50.20aa69
53.65=3.89
55.82s1.7
61.43-236
62.60s322
67.41
$6.22x2.77
74 74.99
SOLT-GNN [32]
48.02+1.77
67.98
71.07:222
60.75e4.00
65.03s412
60.24.2.11
73.58a2.12
Topolmb [71]
52.07a096
56.8420.41
55.47a517
66.48:1.19 66.75:091
69.14s4.3
76.10.0.32
Table D.23: Macro-F1 score (% + standard deviation) of graph classification on manipulated graph datasets with changing imbalance levels over 10 runs " denotes out of memory or time limit. The best results are shown bold.
Algorithm
PTC-MR FRANKENSTEIN PROTEINS
D&D
IMDB-B REDDIT-B ogbg-molhiv COLLAB
Imbalance Ratio: Low
GIN (bb) [63]
18.26.311
54,632098
$9.6 99.672137
63. 63.392034
65.6725.00
66, 142190
58.1
58.45a1 80
SOLT-GNN [32]
43.63
58.54a130
64.60s4.66
62.342066
63.661594 65.71:262
49.17as.76
59.76a1.81
Topolmb [71]
48.87:2.0
53.07an:49
59. 59.9944..3
64.97s1
69.15:3a5
60.91:2.15
Imbalance Ratio: Mid
GIN (bb.) [63] 38. 982597
40.50
56.464290
60.89a1.44
63. 06
67.20
55.05a3.56
63, 13.7792255
SOLT-GNN [32]
36.20
68.52a1
00.58-203
58.6 38.674491
68.73s1
73.24:1.0
Topolmb [7]] 49.17
54.25
59 39.0334.35
64.6521.76
67.98a095
71.52a075
66.58s1.09
Imbalance Ratio: High
GIN (bb.) [63]
34.56s6:32
43.71a1057
53 08.28s
$7 51
59.75sn.69
66.20x2.77
54.389487
64.92s2.1 18
SOLT-GNN
40.70
67.54.228
70.70=2.0
58.50st0.s
64.53a4.8
$4,802325
64.68s2.8)
Topolmh| [71]
-1.65-107
56..8
44.79-1419
63.97-278
66.67-091
68.41-534
65.65in6)
45

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Published as a conference paper at ICLR 2025
Table D.24: AUC-ROC score (% = standard deviation) of graph classification manipulated graph datasets with changing imbalance levels over runs. " denotes out of memory or time limit. The best results are shown in bold.
Algorithm
PTC-MR FRANKENSTEIN PROTEINS
D&D
IMDB-B REDDIT-B ogbg-molhiv COLLAB
Imbalance Ratio: Low
GIN (bb.) [63] $1.36:271
57.3821.66
60. 60.17:2.11
66.09
71. 31,34
78,51=944
63.71asx2
77.4622.0
SOLT-GNN [32]
45.70
72.90.0.24
70.79
68.55
71.2926.5 73.92-3.23
48.18 72.37:208
82.66et.17
Topolmb [71] 49.33s1.9
55.80s0.00
71.26
85.8651.55
82.06e177
Imbalance Ratio: Mid
GIN (bb.) [63]
48.84.2.20
-4.01
53.62+267
67.45-0.66 68, 16
78.44-233
61.33x4.6
86.00e1.22
SOLT-GNN [32]
50.40,2.11
75.83-0.29
76.11:2255
68.57-2.72
76.53:1.52
76.14
87.5
Topolmb [71] 52.09
55.67=1.09
63.96s8.0
72,48-2.37
73.33+200
74.96s1.51
88.27.0.10
Imbalance Ratio: High
GIN (hb.) [63]
49.85.1
56.40-9.37
52.96.275
70.66-0.12
69.92-325
75.86-5.42
58.96.4.55
85. 97..97
SOLT-GNN [32]
47.824375
73.62=1.58
76.43:244
73.57=5.28
70.85+829
84:5.5
81.6
Topolmb [71]
52.26-124
58.29-0.54
61.66+10.19
73.84-1.22
72.55+125
69.04-9.48
87.96-071
Table D.25: Accuracy score (% = standard deviation) of graph classification on manipulated topology-imbalen imbalanced graph datasets with changing imbalance levels over runs. denotes out of memory or time limit. The best results are shown in bold.
Algorithm
PTC-MR FRANKENSTEIN PROTEINS
D&D
IMDB-B
REDDIT-B
COLLAB
Imbalance Ratio: Low
GCN (bb) [21]
51,59
50.53.0.87
65.33+1 as
64.82
69.15s1.44
53.4441.78
64.29.1.41
SOLT-GNN [32]
51.45a312
59.25
65 24
65,69:236
68.23s2.48
37.58
63.824266
Topolmh [71]
46.74.1.57
54.36-048
59.73+5.1
16.18
68. 20
56.94.1.29
60.47-0.9
Imbalance Ratio: Mid
GCN (bb) [21]
50.00s587
50.10
64.32s2.1 68.91 89 49.72a13.46
63.99.2.16
67.95x2xz
67.96.0.89
67.64:2.04
SOLT-GNN [32]
56,23.084
66.42-1.9
62.78.1.35
70.25
61. 61.95+5.55
66, 3.67
Topolmb [?1]
$4.13s4.2
55.38.0.0
64.73,7.09
68.75.076
69.1 290.52
66.48s1.0r
Imbalance Ratio: High
GCN (bb.) [21]
49.9345.00
11.12
58.02a5
60 20.98a6.71
64, 88.2.2
66. 66.38a0.44
68.99
SOLT-GNN [32]
54.78a6.13
68,26.0.28
67 67.38.239
63.2 1a..4
69.80:2.7
67.05a2.54
65.5745.59
Topolmb [7]]
51.81
55.20
54.31s1319
69.662199
66.60sa91
69.09s1.00
67.74
Table D.26: Balanced Accuracy score (% standard deviation) graph classification on ma- nipulated
graph datasets with changing imbalance levels over 10 runs. denotes out of memory or time limit. The best results are shown in bold.
Algorithm
PTC-MR
FRANKENSTEIN PROTEINS
IMDE-B
REDDIT-B
COLLAB
Imbalance Rutio: Low
GCN (bb.) [21]
50.472075
52.46.0.50
61.92s238 61.76x3.57
63.132044
69.15s1.44
53.4421.78
70.14:1.08
SOLT-GNN [32]
48.24s1.00
63.10.0.74
63.81a186 86
43
37.58x3.04
69.49.0.19
Topolmb [71]
50.43
55,53
62.18s200
57.642094
68.20sa.0
56.94.3.23
1a051
Imbalance Ratio: Mid
GCN (bb) [21]
49.74
50.8340.66
61 89
58. 68.2744.65
67.95.283
67. 16.966..8
18.18
SOLT-GNN [32]
51.13
66.62a1.6
67.58 $4.47a6.12
10.1242.7
70.25
15.555
74.88+1.59
Topolmb [?]]
54.34:3.2
54.62a1.00
64.63a3.42
68.75s076
69. 69.12.0.52
74.8720.7
Imbalance Ratio: High
GCN (bb.) [21]
49, 49.96sas4
52,43a1.01
52 22.66x2.17
57.58
64. 8842.2
66.38s0.40
66.80+1.0
SOLT-NN [32]
51.11+1.1
68.06-0.41
66.34-208
60.94+1.6
69.80-2.07
67.05+2.54
74.16x2.61
Topolmb [7]]
72.12
55,50et.13
55.34
66.6344.54
66.60+a91
69.09.1.00
75.02e0019
46

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Published as a conference paper at ICLR 2025
Table D.27: Macro-F1 score (% + standard deviation) of graph classification on manipulated topology hopolog-imbbalanced graph datasets with changing imbalance levels over 10 runs. denotes of memory or time limit. The best results are shown in bold.
Algorithm
PTC-MR FRANKENSTEIN PROTEINS
D&D
IMDB-B
REDDIT-B
COLLAB
Imbalance Ratio: Low
GCN (hb)) [21]
36.7245.8
50.16+1.26
22.088-244
69.02-1.52
49.68-8.r
61.44-1.8
SOLT-GNN [32]
45,00
57.49
61 54.07
63.82:201
07.88
35.0042.77
61.074180
Topolmb [71]
44.72a2.:
54.31
58.672603
55.77a191
67.78s1.00
56.0923.08
58.79+1.01
Imbalance Ratio: Mid
GCN (bb) [21]
40,94s5.67
48. 133,3
1.59211
54,224896
67,80s284
67. 67.18am 181.19
65.45
SOLT-GNN [32]
45.63+4.8
16:16:1.30
67. 67.16:2.05
58.1443.23
70.05-1.19
57.57s8.99
64.70
Topolmb [71]
51,99.3.8
54.34-0.88
40.81+15.22
62.10s6.59
68.6440.77
69.10.o.ee
64.49.a9)
Imbalance Ratio: High
GCN (bb.) [21]
39.32s782
50.84a1.3
51 51.29b1.10
52.46x8.9
63.65a3.15
a5.91
66.80s1.0
SOLT-GNN [32]
39.57as16
67.89
65.88s2.46
60.32a231
69.54:2116
65.40
63. 63.702482
Topolmb [71]
51.43:0.95
$4.99a0.81
44.51x1479
65.6615.25
66.542089
68.76st.17
65.56.0.55
Table D.28: AUC-ROC score (% + standard deviation) of graph classification on manipulated topology-imbalane graph datasets with changing imbalance levels over 10 runs. denotes out of memory or time limit. The best results are shown in bold.
Algorithm
PTC-RR FRANKENSTEIN PROTEINS
D&D
IMDB-B
REDDIT-B
COLLAB
Imbalance Ratio: Low
GCN (bbs) [21]
50.81s2.5
$3.52-0.00
20.005.19
64.25an04
74.69:1.04
50.48:1345
81.8
SOLT-GNN [32]
46.361064
73.17-0.6
59.26x601 67.71s470
65.61.144
74.16.1.8
32.50+5.5
80.89
Topolmb [7]]
52.94.050
56.71
60.66+1.62
74.55+1.00
63.78.2.66
82.674042
Imbalance Ratio: Mid
GCN (hb.) [21]
50.033+4.0
51.66 31.66-0.64
62.02+1 71.33
61.45.4.3
74.23+
74.51
87.46-079
SOLT-GNN [32]
52.54s0.2
72.48a1.32
59.75a4.6
78.21:221
66.93a6.74
86.4 86.4622.4
Topolmh [71]
$7.29.2.45
56.98.1.58
65.7 65.74
74.47-2.4
77.25:0.41
86.74-085
Imbulance Ratio: High
GCN (bb.) [21]
$1.12:1.94
$2.85
47.222545
65.502a.35
68.31s3m
73.4
87.5620.44
SOLT-GNN [32]
49.47a4.66
73.27=0.66
69.84:501
64.79a057
78.04:1.14
72.92at.
86.7741.6
Topolmb [71]
53.65a2.12
57.6620.95
63.26s1224
74.3743.19
71.842107
75.52at.17
88.42a0.13
47

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Published as a conference paper at ICLR 2025
D.2
ADDITIONAL RESULTS FOR ALGORITHM ROBUSTNESS (RQ2)
D.2.1
ROBUSTNESS OF NODE-LEVEL CLASS-MBBALANCED ALGORITIIMS
for class-imbslance
both
for topology-imbbalasee
100
120
Balanced
Low
High
Relative Decrease
Accuracy (%)
Relative Decresse
80
80
60
40
GCN
DRGCN
DPGNN
ImGAGN
GrapISMOTE
GraphENS
GraphMixup
LTE4G
GraphHHA
TAM
TOPOAUC
ReNode
PASTEL
HypelMBA
Figure D.I: Robustness analysis of the node-level algorithms under different class-imbalance degrees on Cora (homophilic). Results are reported with the algorithm performance (Accuracy) and its relative decrease (%) compared to the dlassbbllanced data split (the green bar).
class-imbarn inss-imaalanne
both
topology ianollggyimmullaacce
100
120
Balanced
Low
High
Relative Decrease
100
Relative Decrease (%)
Accuracy (%)
80
-80
70
60
60
40
20
GCN
DRGCN
DPGNN
InGAGN
GrapISMOTE
GraphENS
GrophMizup
LTE4G
GraphSIIA
TAM
TOPOAUC
ReNode
PASTEL
HypalMBA
Figure D.2: Robustness analysis of the node-level algorithms under different class-imbalance degrees on CiteSeer (homophilic). Results are reported with the algorithm performance (Accuracy) and its relative decrease (%) compared to the flas-balanced data split (the green bar).
48

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Published as a conference paper at ICLR 2025
For class-imbaun iimbulance
>
both
4 for topology hongooooy-mmbmceeeem.
80
140
Balanced
Low
High
Relative Decrcase
70
120
Relative Decrease (%)
60
Accurecy (5))
50-
80
40
30-
20
20
GCN
DRGCN
DPGNN
ImGAGN
GrophSMOTE
GraphENS
GraphMixup
LTE4G
GraphSHA
TAM
TOPOAUC
ReNode
PASTEL
HyperIMBA
Figure D.3: Robustness analysis of the node-level algorithms under different class-imbalance degrees on Chameleon (heterophilic). Results are reported with the algorithm performance (Accuracy) and its relative decrease (%) compared to the class balanced data split (the green bar).
for class-imbalance
>/<
both
< for topology-inbaalncee
70
140
Balanced
Low
High
Relative Decrease
60
120
Relative Decrease (%))
Accuracy (%6)
40-
80
30
20
40
10
20
GCN
DRGCN
DPGNN
ImGAGN
GroptSMOTE
GraphENS
GraphMixup
LTE4G
GrophSHA
TAM
TOPOAUC
ReNode
PASTEL
HyperMBA
Figure D.4: Robustness analysis of the node-level algorithms under different class-imbalance degrees on Squirrel (heterophilic). Results are reported with the algorithm performance (Accuracy) and its relative decrease (%) compared to the class-balanced data split (the green bar).
49

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Published as a conference paper at ICLR 2025
D.2.2 ROBUSTNESS OF NODE-LEVEL LOCAL TOPOLOGY-IMBALANCE ALGORITHMS
Cora
Cacarr
PubMMed
Compunxx
70
65
02
72
35
104
10gb
18gh
20
Poeto
Chamdlon
Squinel
33
40
14.0
35
43-
13
OraphPaccher
Figure D.5: Robustness analysis of the node-level algorithms under different local topology- imbalance degrees (Low, Mid, and High). Results reported with the algorithm performance (Accuracy) with the standard deviation error area.
D.2.3 ROBUSTNESS OF NODE-LEVEL GLOBAL TOPOLOGY-IMBALANCE) ALGORITHMS
Cor
Chebeer
Coaputers
Photo
87
(h)
90
65
1.70
10g3
18g
18:g
High
Chanteleu
Squirel
14
35
28-
30
22
-Q- OCN
-F0
BaNode
- PASTEL
-0-
RyperDABA
-Q-
TAM
-9
TOPOAUC
GlaphENS
CaapiSEA
Figure D.6: Robustness analysis of the node-level algorithms under different global topology- imbalance degrees (Low, Mid, and High). Results are reported with the algorithm performance (Accuracy) with the standard deviation error area.
50

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Published as a conference paper at ICLR 2025
D.2.4 ROBUSTNESS OF GRAPH-LEVEL CLASS- IMBSLNND ALGORITHMS
PTC-MR
FRANKENSTEIN
PROTTFINS
DAD
30
30
30
43
Ddlacad
Talared
IMD6-
72
52
62
50
12
Balased
Lawe
1065
Balaaedd
Bataced
6'ONN
Topalmb
Figure D.7: Robustness analysis of the graph-level algorithms under different class-imbalance degrees (Low, Mid, and High). Results are reported with the algorithm performance (Aceuracy) with the standard deviation error area.
D.2.5 ROBUSTNESS OF GRAPII-EVEL TOPOLOGYY-MBALANCED ALGORITIMM
PIT-MR
FRANKENSTEIN
PROTFINS
DAD
55
02
90
55-
50
57.5
50
41
40
Md
62
63
SOLT-ONN
Figure D.8: Robustness analysis of the graph-level algorithms under different topology-imbalance degrees (Low, Mid, and High). Results reported with the algorithm performance (Accuracy) with the standard deviation error area.
51

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Published as a conference paper at ICLR 2025
D.3 ADDITIONAL RESULTS FOR VISUALIZATIONS (RQ3)
D.3.1 VISUALIZATIONS OF NODE-LEVEL ILAAANNDBALANCED ALGORITHMMS
GCN
DRGON
DPONN
ImGAGN
Silhouelte Score: 0.26
Silhouette Score: 0.31
Silhouette Score: 0.19
Silhouette Score: 0.21
GraphSMOTE
GraphENS
GraphMixup
LTE4G
Silhouette Score: 0.31
Silbouette Score: 0.36
Silbouette Score: 0.25
Silhouette Score: 0.38
TOPOАUC
GraphSHAA
Silhouette Score: 0,36
Silhouette Score: 0.31
Silhouette Score: 0,33
Figure D.9: Visualizations of the embedding for node-level class-imbalanced algorithms.
D.3.2 VISUALIZATIONS OF NODE-LEVEL LOCAL TOPOLOGY-IMBALANCED ALGORITTMS
GCN
DEMO-Net
meta-tail2vee
Tail-GNN
Silbouette Score: 0.25
Silhouette Score: 0.20
Silhouette Score: -0.28
Silhouette Score: 0.16
Cold Brew
LTE4G
RawlsGCN
Graph Patcher
Silhouette Score: 0.12
Silhouette
Silhouette Score: 0.18
Silhouette
Figure D.10: Visualizations of the embedding for node-level local hopology-imbalane algorithms.
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Published as a conference paper at ICLR 2025
D.3.3 VISUALIZATIONS OF NODE-LEVEL GLOBAL TOPOLOGY-IMBALANCED ALGORITHMS
GCN
ReNode
TAM
PASTEL
Silhouette Score: 0.31
Silhouette Score: 0.31
Silhouette Score: 0.35
Silhouette Score: 0.33
TOPOAUC
Hyperl
Silhouette Score:
Silhouette Score: 0.18
Figure D.11: Visualizations the embedding for node-level global topology-imbalanced algorithms.
D.3.4 VISUALIZATIONS OF GRAPII-EVEL CLASS-IBBLLANCED ALGORITIMMS
GIN
G'GNN
Topolmb
DataDec
Silbouette Score: 0.43
Silhouette Score: 0.55
Silhouette Score: 0.64
Silhouette Score: 0.52
Figure D.12: Visualizations of the embedding for graph-level class-imbalanced algorithms.
D.3.5 VISUALIZATIONS OF GRAPH-LEVEL TOPOLOGY-IMBBLLNCEED ALGORITHMS
GIN
SOLT-GNN
Topolmb
Silhouette Score: -0.35
Silhouette Score: -0.18
Silhouette Score: -0.32
Figure D.13: Visualizations of the embedding for global-level topology-imbalancee algorithms.
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Published as a conference paper at ICLR 2025
D.4 ADDITIONAL RESULTS FOR EFFICIENCY ANALYSIS (RQ4)
D.4.1 EFFICIENCY ANALYSIS OF NODE-LEVEL CLASS-MBBALANCED ALGORITIMMS
Actor (Low)
Actor (Low)
CraptSMOTE Limphhisup
GuppENS
LIEAU TOPUAEU DROUN
LIEAS
GapaENS
Accurccy (16
24
IoGAAN
Accuroyy (%)
24
ImUAIN
GopRSMOTT
GCN
SmA
GInOSSIA
23
DPUNN
21
20
30
40
50
60
70
80
90
21
500
1000
1500
2000
2500
Training Time (s)
Training Space (MB)
Figure D.14: Time and space analysis node-level class-imbalanced IGL algorithms on Actor
oghn-arXiv (Low)
ogbn-arXiv (Low)
59
60
GCN
GrspiSHA
x DRROKN (UUM)
DPGNN (OOM)
60
59
GCN
GmphSSHA
Accurscy (%)
58
InGIAGN (OOM)
URpESMOTE (00M)
DRGCN
DPUNN (OOM)
57
LTTAG (D0M)
Accurcyy
56
55
GruptaKirup
TOPOAUC
36
GraphMiig
GROASMOTE
(OOM)
1AM
53
UnphtnS
GaapEENS
1200
1400
1600
1800
2000
2200
2000
4000
6000
8000
10000
12000
14000 16000
Training
(5)
Training Space (MB)
Figure D.15: Time and space amalysis of node-level class- iasalanbbln IGL algorithms ogbn-ar Xiv.
D.4.2 EFFICIENCY ANALYSIS NODE-LEVEL LOCAL ALGOORITHMS
Actor (Mid)
Actor (Mid)
36
36
Cold Brew
Cold Brew
Accunccy (%)
(%6
31
21
DEMO--ee
RawisUKU
DEMO-Na
26
Tail-NNN
26
Tail-GNN
LTEAG
GappPaucceer
GmmpiPatccar
21
GGN
1000
2000
3000
4000
5000
21
OCN
2000
4000
6000
8000
Training Time
Training Space (MB)
Figure 1.16: Time and space analysis of node-level local topology-imbalancee IGL. algorithms on
Actor
ogbn-arXiv (Mid)
ogbu-arXiv (Mid)
Cold Hnew
G'THEEGNN (UKM)) CrgghPuthhe
THI-GNN (UUM)
Ascurac (%)
DEMIO-Ns
GraphPuscher
DEMO-NA
60
60
55
Accuncc
$5
GCN
so
GCN
t
40
40
RawisGUN
5000
10000
15000
20000
25000
30000
5000
10000
15000
20000
25000
30000
Training Time (s)
Training Space (MB)
Figure D.17: Time and space analysis of node-level local hopology-imbalann IGL algorithms ogbn-arXiv.
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Published as a conference paper at ICLR 2025
D.4.3 EFFICIENCY ANALYSIS OF NODE-LEVEL GLOBAL TOPOLOGY- IMBLLACEED
ALGORITHMS
Actor (High)
Actor (High)
PASTEL
PASTEL
Accuracy (%)
26
26
HyporMMiA
Accurscy
25
25
23
TOPOATIC
TAM
ReNode
22
DCN
200
400
600
800
1000
1200
22
2500
5000
7500
10000
12500
15000
17500
Training Time (9)
Training Space (MB)
Figure D.18: Time and space analysis of node-level global aapology-imbblaneed IGL algorithms on Actor
ogbn-arXiv (High)
ogbn-arXiv (High)
TAM
TAM
Accaracy (%)
PASTEL (OOM)
TOPOADC (0OM)
TOPOAEC (OOM)
51
GUN
HypelMBA (OOM)
Accuracy
GCN
HyperiMIIA
ReNodl
Triining
Training Space (MB)
Figure D.19: Time and space analysis of node-level global topology-imbalance IGL algorithms on ogbn-arXiv.
D.4.4 EFFICIENCY ANALYSIS OF GRAPH-LEVEL. CLASS-IMBALANCED ALGORITHMS
COLLAB (Low)
COLLAB (Low)
73
DanaDe:
Dataile
Topolmb
Accuracy (16)
66
Topolmb
Accumcc (%))
66
61
GFONN
GEGNN
lm0KB
Im0KKB
51
100
200
300
400
500
40
60
80
100
120
140
160
Training Time (s)
Training Space (MB)
Figure D.20: Time and space analysis graph-level class-imbalanced IGL algorithms on COLLAB.
D.4.5
EFFICIENCY ANALYSIS OF GRAPH-LEVEL. TOO.AAAAAAADOO...AAAAAAAAAAAAA ALGORIITMS
COLLAB (Mid)
COLLAB (Mid)
GIN
Accurscy (%)
64
Accuncy (%)
64
62
62
SOLT GNNT-
60
60
58
58-
Topolmb
Topolib
56
0
500
1000
1500
2000
2500
200
400
600
800
1000
1200
Training Time (5)
Training Space (MB)
Figure D.21: Time and space analysis of graph-level topology-imbalancee imbalanced IGL algorithms on COLLAB.
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Published as a conference paper at ICLR 2025
Imbalance Manipulator
IGL Algoriths
Package Utils
Datasets
Node-Level Class- banss-mmbllacee Algoridhm
Hyperparameter Tunning (wandb Sweeps)
Node-Level
Graeh-Level
Node-Level Copoloy--mballncee Algorithm (Local and Global)
User-Defined Datasets
Workflow Automation
Configuration
Graph-Lovel Clas--Iiballnced Algorithm
Evaluation Metric
Level Class-Ibbllace
Graph-Lva Level Clas--mballnce
Graph-Level Topology-Imbalance Imbalanced Algorithm
Dashboard
Node- Lvel Topology Imbalance
Gruph-1 evel
Tapology Imbulance
Uxer-Defined Algorithms
Experiment Trace
Experiment Report
GNN Backbones
GCN
GAT
GIN
GraphSAGE
User-Defined GNNs
Weights Saving
Figure E.I: The package structure of which mainly consists of four modules.
E PACKAGE AND REPRODUCIBILITY
Package. We established and released a comprehensive Imbalanced Graph Learning Benchmark (IGL-Bench) package, which serves as the first open-sourced bench- mark for graph-specific imbalanced learning to the best of our knowledge. IGL-Bench encompasses 24 state-of- the-art IGL algorithms and 17 diverse graph datasets cov- ering node-level and graph-level tasks, addressing class- and aapoloyy-imbalane
GLG
Imbalanced Graph Learning Benchmark
issues, while also adopting con- sistent data processing and splitting approaches for fair comparisons over multiple metries with different focus.
Figure E.2: The IGL-Bench package.
As shown in Figure 1, 1, the TGI-Bench package is mainly composed of four modules. ! The Imbalance Manipulator module performs different types of imbalance manipulations for the imbalance ratio on the built-in 17 node-level datasets, graph-level datasets, or user-defined datasets according to user configurations.
The IGL Algorithms module has 24 state-of-the-arr algorithms built-in and also supports calling user-defined IGL algorithms. ① The GNN Backbones module supports variety of mainstream GNNs and also allows for user-defined GNNs. + The Package Utils module offers variety of utility tools, enhancing the usability and benchmarking efficiency of the package.
Documentation and Uses. We have made concerted effort to provide users with comprehensive documentation ensure the seamless use of the package. Additionally, we have included necessary comments to enhance code readability. We supply the required configuration files reproduce the experimental results, which also serve examples of how to use the package effectivelyy
License. Our package (codes and datasets) is licensed under the MIT License. This license permits users to freely use, copy, modify, merge, publish, distribute, sublicense, and sell copies of the software, provided that the original copyright notice and permission notice are included in all copies substantial portions of the software. The MIT License is widely accepted for its simplicity and permissive terms, ensuring ease of use and contribution to the codes and datasets. We bear all responsibility in case of violation of rights, etc, and confirmation of the data license.
Code Maintenance. We are committed to continuously updating our code and actively addressing users' issues and feedback. Additionally, we warmly welcome community contributions to enhance our library and benchmark algorithms. Nonetheless, we will enforce strict version control measures ensure reproducibility throughout the maintenance process.
hhttps://gi thub. http:/iiinnnnttttttttttec httptt.coo///mggggissss/c////// Hench.
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F FURTHER DISCUSSIONS
F.1 RELATED WORKS
Benchmarking is widely used in reviews and standardized evaluations of particular field, providing unique insights (Sun et al., 2024). To the best of our knowledge, there exists no established benchmark specifically dedicated to evaluating imbalanced learning graphs. Our BELcB represents the foundational effort in this domain, encompassing both node-level and graph-level challenges related to class- and appoloyyiimallane the broader landscape of imbalanced graph learning. We position our work in relation to notable surveys in the field.
This section compares and contextualizes our contributions within
Liu et al. (2023b) comprehensively reviews the landscape of imbalanced learning on graphs, outlining key terminologies and taxonomies related to problem types and solution strategies. It establishes foundational understanding crucial for addressing skewed data distributions in graph-based tasks.
Focused on the challenges of GNNs in practical applications, Ju et al. (2024b) addresses imbalance in data distribution and the robustness against noise, privacy concerns, and -f-ttsiibitttiinnnnn scenarios. It highlights solutions that enhance the reliability of GÑNs in real-world settings.
Ma et al. (2023) specifically explores maassiimbllncced learning on graphs, emphasizing the integra- tion of graph representation learning with imbalanced learning techniques. provides a taxonomy of existing works and outlines future directions in the evolving field of graph class-imbalanced learning.
In contrast to these surveys, our IGL-Bench offers practical benchmarking package tailored explicitly for imbalanced graph learning. By systematically evaluating the performance of algorithms across various imbalance types, IGL-Bench provides a standardized package for assessing the efficacy and robustness of existing and future methods in this emerging field. While existing surveys establish the theoretical underpinnings and methodological approaches imbalanced learning on graphs, Behch offers a concrete tool for empirical validation and comparison. This practical focus enables researchers and practitioners to not only understand the theoretical aspects but also to apply and benchmark algorithms effectively across diverse real-world graph datasets.
In summary, our work fills a critical gap by introducing IGL-Bench as the first benchmarking suite tailored for imbalanced graph learning, thereby advancing the state-of-the-art in the field and fostering deeper insights into the challenges and opportunities imbalanced graph data analysis.
F.2 LIMITATIONS
IGL - -Bnchh has some limitations that we aim to address in future work.
We hope to include broader range of datasets evaluate algorithms in different scenarios. Our current datasets are predominantly homogeneous graphs, which do not fully capture the diversity and complexity of real-world networks. Many IGL methods struggle with complex graph types, such as heterogeneous graphs with multiple types of nodes and edges. Including such datasets would provide a more robust evaluation of these algorithms and highlight their strengths and weaknesses.
We hope to implement more IGL algorithms for various tasks, such as few-shot classification, dynamic graph learning, and anomaly detection, etc. Our current benchmark is limited to a specific set of tasks, which might not reflect the full potential and versatility of IGL methods. By expanding the range of tasks, we can gain a deeper understanding of the progress in the field and provide insights into how different algorithms perform across diverse applications.
Due to resource constraints and the availability of implementations, we could not include some of the latest state-of-the-art IGL algorithms in our benchmark. This might impact the comprehensiveness of our evaluation, as some promising methods are not represented. We aim to address this by continuously updating our package and incorporating these algorithms they become available.
Our current evaluation framework primarily focuses on the performance metrics of the algorithms. However, practical aspects such scalability, computational efficiency, and memory usage also crucial for real-worle applications. We plan to include these factors in future evaluations to provide a more holistic view of each algorithm's practicality and efficiency.
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Published as a conference paper at ICLR 2025
We will continuously update repository to keep track of the latest advances in the field. We also open to any suggestions and contributions that will improve the usability and effectiveness of our benchmark, ensuring it remains valuable resource for the IGL research community.
F.3 DATASET PRIVACY AND ETHICS
We ensured all datasets were sourced from publicly available repositories with explicit research permissions. For user-generated or social platform data, we rely on terms including research consent. We anonymized Personally Identifiable Information (PII) and screened for offensive content, though complete risk elimination remains challenging. Users are urged use datasets responsibly and be mindful of ethical implications.
terms of negative social impact, we believe our work does not pose potentially significant negative societal impact to the best of our knowledge. Our research is primarily focused on benchmarking graph learning algorithms in the context of imbalanced data. However, we remain mindful of ethical considerations and will continue to monitor any broader implications
work progresses.
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Reviews:
[{"review_id": "plAfsMgV1E", "reviewer": "Reviewer_6GyC", "summary": "This paper addresses the gap in graph learning by introducing a benchmark named IGL-Bench for imbalanced graph learning. The benchmark covers 24 algorithms across 17 datasets, tackling node-level and graph-level tasks that are affected by class and topology imbalances. The benchmark includes standardized data processing, evaluation protocols, and metrics across different datasets. Evaluation on effectiveness, robustness, boundary clarity, and efficiency of IGL methods under imbalanced conditions are further carried out. The benchmark findings reveal key insights into the strengths and limitations of current IGL algorithms, particularly around scalability, robustness, and their dependency on graph topology properties.", "questions": "- Can the authors elaborate on the specific challenges encountered in standardizing data splits and evaluation protocols across such a diverse set of IGL methods?\n- How does IGL-Bench handle algorithm hyperparameter tuning, particularly for methods that might be sensitive to different types of imbalance?\n- Are there future plans to study the scalability within IGL-Bench, e.g., for larger, more complex graph datasets?", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- Originality: The paper introduces a comprehensive benchmark for IGL to fill the gap in graph learning.\n- Quality: Experiments valiadate the quality of the benchmark.\n- Clarity: The paper is well written and organized. Easy for general audience to follow.\n- Significance: The benchmark provides an easy platform for developing or comparing IGL methods, especially as graph learning expands into real-world, imbalanced datasets.", "weaknesses": "- Complex visualizations: Certain visualizations, such as multi-metric plots across multiple imbalance ratios, could benefit from clearer explanations to aid interpretability for readers less familiar with the metrics.\n- New dataset: No new dataset is introduced in the paper.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "LNYNHrzTxt", "reviewer": "Reviewer_t4gw", "summary": "This work presents a benchmark for imbalanced graph learning, encompassing 17 graph datasets and 24 imbalance-handling algorithms, along with a unified data processing pipeline, splitting strategy, and evaluation protocols. The benchmark addresses questions related to effectiveness in handling imbalance, robustness across different imbalance ratios, and efficiency in terms of time and space for both node-level and graph-level tasks. Additionally, an open-source codebase is provided to facilitate reproducible evaluations.", "questions": "See Weakness.", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Benchmarking imbalanced graph learning is important to track progress in the research community.\n2. The four research questions posed are relevant and of interest to the community.\n3. The paper is well-written and easy to follow.\n4. The experiments are thorough and well-designed. The availability of open-source code enhances reproducibility and accessibility.", "weaknesses": "1. For node-level class-imbalanced algorithms, it would be beneficial to include traditional methods for addressing class imbalance, such as reweighting or PC Softmax [1], to provide a comprehensive comparison. Additionally, reporting per-class F1 scores could offer more insights into model performance across majority and minority classes, enabling a more detailed analysis of effectiveness.\n\n2. Some findings lack depth and do not offer clear insights. For instance, the observation that most algorithms perform poorly on the large-scale ogbn-arXiv dataset is presented without an explanation. It would be valuable to investigate and discuss the reasons for this poor performance, especially through additional experiments.\n\n3. In Section 4.4, which assesses the efficiency of different models, the experiments are conducted on the Cora dataset, the smallest of the datasets used. This setup makes the time and space usage of the algorithms highly dependent on implementation details rather than their inherent algorithmic complexity. While the Appendix includes results for the ogbn-arXiv dataset, they cover only a subset of models, as other models encountered memory limitations. A theoretical analysis of the algorithms' complexities would provide a more meaningful comparison of their efficiency. Relying solely on runtime measurements can be misleading, as they may be influenced by implementation optimizations and do not necessarily reflect the algorithms' underlying efficiency.\n\n4. On the ogbn-arXiv dataset, certain resampling algorithms, such as GraphENS and GraphSHA, run successfully, whereas others, like GraphSMOTE, encounter memory issues. It is unclear whether this is due to differences in algorithmic complexity or specific implementation choices. Given the similarity of these resampling approaches, clarifying whether the issue arises from inherent algorithm characteristics or particular implementation choices would be helpful.\n\n[1] Disentangling label distribution for long-tailed visual recognition. CVPR. 2021.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "rpeByN4xyQ", "reviewer": "Reviewer_mZgm", "summary": "This paper introduces a benchmark for Imbalanced Graph Learning (IGL). IGL-Bench offers a unified framework for evaluating 24 IGL algorithms across 17 datasets, addressing both class- and topology-imbalance at node and graph levels. The authors conduct a rigorous evaluation on effectiveness, robustness, and efficiency, providing a comparative analysis of existing methods. Additionally, the paper presents an open-source package to facilitate reproducible research and encourage further development in the IGL field.", "questions": "1.\t How does the benchmark incorporate, or plan to incorporate, recent advances in IGL (see weaknesses), and evaluate whether these general approaches improve performance, robustness, and other metrics?\n2.\tAre there any plans to provide an API reference for IGL-bench? This would significantly enhance usability.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "-\tThe proposed IGL-Bench is well-constructed, it can provide a standardized testbed for future work, encouraging a more consistent evaluation process for IGL.\n-\tThe paper is well-written and easy to follow. The authors' thorough analysis of the benchmarking results leads to interesting insights.", "weaknesses": "Recently, several more general IGL methods have been proposed, which can be used independently or in combination with the IGL techniques discussed in this paper. For instance, [1] based on topological augmentation and automated loss engineering approach [2], both presented at ICML '24, are notable examples. It would be beneficial if IGL-bench could include these recent booster-type methods and provide related discussion.\n[1] Liu, Zhining, et al. \"Class-Imbalanced Graph Learning without Class Rebalancing.\" Forty-first International Conference on Machine Learning.\n[2] Guo, Xinyu, et al. \"Automated Loss function Search for Class-imbalanced Node Classification.\" Forty-first International Conference on Machine Learning.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Spotlight)