Homophily Enhanced Graph Domain Adaptation
Authors: Ruiyi Fang
Bingheng Li
Jingyu Zhao
Ruizhi Pu
QIUHAO Zeng
Gezheng Xu
Charles Ling
Boyu Wang
Venue: ICML 2025 poster (2025)
Keywords: Graph Domain Adaptation
Transfer Learning
Primary area: general_machine_learning->transfer_multitask_and_metalearning

Abstract: Graph Domain Adaptation (GDA) transfers knowledge from labeled source graphs to unlabeled target graphs, addressing the challenge of label scarcity. In this paper, we highlight the significance of graph homophily, a pivotal factor for graph domain alignment, which, however, has long been overlooked in existing approaches. Specifically, our analysis first reveals that homophily discrepancies exist in benchmarks. Moreover, we also show that homophily discrepancies degrade GDA performance from both empirical and theoretical aspects, which further underscores the importance of homophily alignment in GDA. Inspired by this finding, we propose a novel homophily alignment algorithm that employs mixed filters to smooth graph signals, thereby effectively capturing and mitigating homophily discrepancies between graphs. Experimental results on a variety of benchmarks verify the effectiveness of our method.

Homophily Enhanced Graph Domain Adaptation
Ruiyi Fang
Bingheng Li
Jingyu Zhao?
Ruizhi Pu' Boyu Wang"
Qiuhao Zeng' Gezheng Xu' Charles Ling 14
Abstract
by leveraging deep domain adaptation techniques (Shen et al., 2020b; Wu et al., 2020). While these approaches have achieved promising results in GDA (Yan & Wang, 2020; Shen et al., 2023), their efforts are centered on mitigating the discrepancy in structural and attribute distributions.
Graph Domain Adaptation (GDA) transfers knowledge from labeled source graphs to unla- beled target graphs, addressing the challenge of label scarcity. In this paper, highlight the significance of graph homophily, pivotal fac- tor for graph domain alignment, which, however, has long been overlooked in existing approaches. Specifically, our analysis first reveals that ho- mophily discrepancies exist benchmarks. More- over, we also show that homophily discrepancies degrade GDA performance from both empirical and theoretical aspects, which further underscores the importance of homophily alignment in GDA. Inspired by this finding, we propose a novel ho- mophily alignment algorithm that employs mixed filters to smooth graph signals, thereby effectively capturing and mitigating homophily discrepancies between graphs. Experimental results on vari- cty of benchmarks verify the effectiveness of our method.
ACM3
EUROPE
ACM4
Density
BRAZIL
Denaity
0.25
0.25
0.75
Rade
(a) Airport dataset
(b) ACM dataset
Figure 1. This represents node homophily distibution in two bench- mark. The dotted line represents the overall node homophily ratio of the entire graph. This shows the local node homophily dis- tibution shift is existing in various levels of homophilic groups. Homophily means that similar nodes are prone connect each other.
In this work, we highlight the role of graph homophily dis- crepancies and their impact on GDA performance. Specif- ically, we investigate the local homophily distribution of graph on two GDA benchmarks, as shown in Figure 1. It can be observed that while the overall homophily distribu- tion discrepancy of the graph is relatively small, the dis- crepancy within homophilic and heterophilic subgroups is more substantial. For example, as shown in Figure (a), the overall graph node homophily ratio between ACM3 and ACM4 appears relatively similar, and the distribution of homophilic and heterophilic groups varies more substan- tially. To further investigate its impact on GDA, we conduct another experiment to explore how the homophilic ratio affects the cross-network performances, as shown in Fig- ure 2. It can be observed that the classification accuracy of target graph nodes exhibits a negative correlation with homophily divergence across different homophily ratios in datasets, which indicates the importance of separately dealing with heterophilic and homophilic groups. Besides, this observation also suggests that the discrepancies ho- mophilic distributions between source and target graphs may significantly impact target node classification perfor-
1. Introduction
In the era of massive graph data collection, graphs often integrate both structural topology and node attributes, pro- viding rich contexts for numerous real-world applications. However, they are often constrained by label scarcity, as an- notating structured data remains challenging and costly (Xu al., 2022; 2024b; Zeng et al., 2024; 2023). To address this challenge, Graph Domain Adaptation (GDA) has emerged as an effective paradigm to transfer knowledge from la- beled source graphs to unlabeled target graphs (Chen et al., 2019; Shi et al., 2024). Conventional GDA methods pri- marily focus on aligning graph structures across domains
'Equal contribution 'Western University, Ontario, Canada MMichiaan State University, Michigan, USA University of Elec- tronic Science and Technology of China, Chengdu, Sichuan Province, China 4 'Vector Institute, Ontario, Canada. Correspon- dence to: Boyu Wang dowang@csd.uwoo.
Proceedings of the 42nd International Conference Machine Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

---

Homophily Enhanced Graph Domain Adaptation
mance, thereby highlighting the importance of mitigating homophily divergence.
Liu al., 2025; Li al., 2024a; 2025a; Luan al., 2022; Huang al., 2023; 2024; Zhuo al., 2025; 2024b) reveal that graph homophilc and heterophilic patterns impact graph clustering performance between the test and training sets. However, the above methods failed to explore the role of homophily in GDA and minimize their discrepancy in many aspects (Kang et al., 2024; Pu et al., 2025; Xu et al., 2025; Xie al., 2024; 2025).
To further justify this implication, we theoretically investi- gate the generalization performance of GDA from the PAC- Bayes perspective. Specifically, we show that the target loss can be upper bounded in terms of homophilie signal shift, heterophilic signal shift, attribute signal shift and graph node heterophily distribution shift. This aligns with our empiri- cal findings, suggesting that discrepancies in graph signals should be addressed separately. To this end, we propose novel cross-channel graph homophily enhanced alignment (HGDA) algorithm for cross-network node classification, as pass,
2.2. Graph Domain Adaptation
Recent Domain Adaptation works have differences from GDA methods (Li et al., 2024b; Chen et al., 2024; Li et al., 2025c; 2024c; 2025b; Zeng et al., 2025; Xu et al., 2024a). Identifying the differences between the target and source graphs in GDA is crucial. For graph-structure data, sev- eral studies have explored cross-graph knowledge transfer using graph domain adaptation (GDA) methods (Shen & Chung, 2019; Dai et al., 2022: Shi et al., 2024). Some graph information alignment- based methods (Shen et al., 2020a;b; Yan & Wang. 2020; Shen al., 2023; Yang et al., 2023a) adapt graph source node label information by in- tegrating global and local structures from both nodes and their neighbors. UDAGCN (Wu et al., 2020) introduces a dual graph convolutional network that captures both lo- cal and global knowledge, adapting it through adversarial training. Furthermore, ASN and GraphAF. (Zhang et al., 2021; Guo al., 2022) consider extracting and aligning graph specific information like node degree and edge shift, enabling the extraction of shared features across networks. SOGA (Mao et al., 2024b) is the first to incorporate dis- criminability by promoting structural consistency between target nodes of the same class, specifically for source- fource-free domain adaptation (SFDA) on graphs. SpecReg (You et al., 2022) applies an optimal transport-based GDA bound and demonstrates that revising the Lipschitz constant of GNNs can enhance performance through spectral smoothness and maximum frequency response. JHGDA (Shi et al., 2023) tackles hierarchical graph structure shifts by aggregating domain discrepancies across all hierarchy levels to provide a comprehensive discrepancy measure. ALEX (Yuan et al., 2023) creates hhbel-shfft-ehhaane augmented graph view using a low-rank adjacency matrix obtained through sin- gular value decomposition, guided by contrasting loss function. SGDA (Qiao et al., 2023) incorporates trainable perturbations (adaptive shift parameters) into embeddings via adversarial learning, enhancing source graphs and min- imizing marginal shifts. PA (Liu et al., 2024c) mitigates structural and label shifts by recalibrating edge weights to adjust the influence among neighboring nodes, addressing conditional structure shifts effectively.
shown in Figure 3. HGDA utilizes homophilic, full- full-pass, and heterophilic filters to separately extract and align the homophily signal, heterophily signal, and attribute signal for both the source and target domains.
Our contributions are summarized as follows:
Empirical insights: We first highlight the significance of homophily distribution discrepancy in GDA and empirically examine its impact on GDA performance.
Theoretical justification: We theoretically justify the impact of homophily distribution shift on GDA and demonstrate that this discrepancy can be mitigated by addressing homophilic and heterophilic groups sepa- rately.
Algorithmic framework: Inspired by theoretical in- sights, we propose HGDA, which mitigates homophily distribution shifts by aligning and capturing homophily, heterophily, and attribute signals.
2. Related Work
2.1. Heterophilic Graph Learning
Heterophilic structure is prevalent in practice, from personal relationships in daily life to chemical and molecular scien- tific study (Fang et al., 2022: He et al., 2025). Developing powerful heterophilic GNN models is hot research topic. (Lim et al., 2021; Qian et al., 2024; Yang et al., 2024a; 2023b; Zhuo et al., 2024c; Li et al., 2025b) provide general benchmarks for heterophilic graph learning. In addition, many methods have been proposed to revise GNNs for het- erophilic graphs. (Yang et al., 2021) specifies propagation weight for each attribute to make GNNs fit heterophilic graphs and (Li et al., 2022a) explores the underlying ho- mophilic information by capturing the global correlation of nodes. (Zhu et al., 2020a) enlarges receptive field via exploring high-order structure. (Chien et al., 2021) adap- tively combines the representation of each layer and (Chen et al., 2020) integrates embeddings from different depths with residual operation. Recent studies (Mao et al., 2024a;
2

---

Homophily Enhanced Graph Domain Adaptation
USA
Notert Diference
1:54
Porcent Eiffrannc
66
100
SRAZK
[-U
0-10
60
76
ejoz
P4 07.00
enal
8143
dog
farge
Himopply Aato Aango
(a) U+ E
(b) U+ B
(c) E
(d) A3 ++ A4
Figure 2. Performance of cross-network classification tasks in different homophilic ratio ranges. For a fair comparison, we use a two-layer GCN with standard unsupervised GDA settings our evaluation model. The X-axis represents node subgroups categorized by specific ranges of homophily ratios. The bars in the vertical bar chart represent the proportion of nodes in each subgroup, defined by a specific homophily ratio range relative to the total number of nodes in the graph (left Y-axis). The line chart in the figure above represents the difference in the proportion of nodes in each subgroup between the corresponding upper and lower graphs (upper right Y-axis). The line graph in the figure below represents the target node classification accuracy for two corresponding tasks in each subgroup with different homophily ratios (lower right Y-axis). We observe that homophily divergence has negative correlation with target node classification accuracy across various homophily ratios.
3. Empirical and Theoretical Study
node v and yi is the node label.
3.1. Notation
3.2. Empirical Insight
An undirected graph G = 1,, consists of set of nodes V and edges E, along with an adjacency ma- trix A, a feature matrix X, and a label matrix Y. The adjacency matrix A E NxN encodes the connections be- tween N nodes, where Asp- nodes and j. and Asj = 0 means the nodes are not con- nected. The feature matrix X e Nxd represents the node features, with each node described by d-dimensional fea- ture vector. Finally, Y E R.C contains the labels for the N nodes, where each node is classified into one of C classes. Thus, the symmetric normalized adjacency matrix À = (D + 1) 1 (A + () + 1)- and the normal- ized Laplacian matrix is L = I- Å. In this work, we explore the task of node classification in a unsupervised setting, where both the node feature matrix X and the graph structure A are given before learning. Now we can de- fine source graph G = (VS 88, AS X graph GJ (vT, NOT,ETTAA AF,x".
To futher explore node homophily ratio distribution shifts on the aforementioned datasets in Figure we evaluate the effecctiveness of GDA on different homophily subgroups. To evaluate the homophily divergence effect to GDA, we conduct an examination of node subgroups with different homophilic and heterophilic groups. The following exper- iments are conducted on two common graph benchmark airport datasets with unsupervised GDA node classcification task. Specifically, we focus on how the homophily discrep- ancy between the source and target graphs affects the per- formance of node classification on the target graph. Figure shows the classification accuracy for different homophily ratio subgroups. Experimental results four datasets presented in Figure 2. It can be observed that the classi- fication accuracy of target graph nodes negatively corre- lates with homophily divergence across heterophilic and homophilic groups in the datasets. For example, as shown in Figure 2 (d), subgroups within homophily divergence in the 0.0-0.1 (heterophilic groups) and 0.9-1.0 (homophilic groups) ranges exhibit high discrepancies in terms of differ- ence in the proportion (orange line), which leads to low node classification accuracies on the corresponding target sub- groups (red and purple lines). Our observations suggest that the homophily discrepancy between the source and target graphs in corresponding subgroups has a significant impact on GDA performance. This highlights the importance of mitigating the homophily divergence in both homophilic and
indicates an edge between
A y and target
Local node homophily ratio is widely used metric for quantifying homophilic and heterophilic patterns. It is de- fined as the proportion of node's neighbors that share the same label as the node (Pei et al.; Zhu et al., 2020b; Li et al., 2022b; Miao et al., 2024). It is formally defined as
Hu u No. Vu yo
H" Woode
(1)
Nel
where where N, denotes the set of one-hop neighbors of
3

---

Homophily Enhanced Graph Domain Adaptation
heterophilic groups for GDA. Additional results on more datasets are shown in Appendix C.
Definition 3 (KL Divergence Between Graph Heterophily
Distributions). Let GS and GD be two graphs from different domains with heterophily distributions: P (h), PK (h) > for all h. The Kallback-eeibler (KL) divergence benween P and Pf is defined as:
3.3. Theoretical Analysis
In this subsection, we will propose theoretical evidence based on the PAC-Baysian framework to verify the ho- mophily divergence effect GDA performance and demon- strate the effectiveness of our proposed method. To effec- tively evaluate the performance of a deterministic GDA classifier on structured graph data, we introduce the notion of margin loss.
PS (h) P
DEL (P [PP)
Σ
PS PS (h) log
(6)
NEW
where H. is the set of possible node heterophily values. Theorem 1 (Domain Adaptation Bound for Deterministic Classifiers). Let & be family of classification functions. For any classifier & in 4, and for any parameters X > O and y 2 O, consider any prior distribution P over &b that is independent of the training data VS. With a probability of at least ô over the sample Y for any distribution Q on & such that the following inequality holds:
Margin loss on each domain. We can define the empirical and expected margin loss of classifier Φ E T on source graph G and target graph G Given Y', the empirical margin loss of @ on G for a margin 7 2 0 is defined as:
[3(0)
Ns iEVS
1 Σ
1 + (2) S Zg(0) +
2(Dk) +
1
+
4Ns
A
1 1 .C))).)))l
ApCCo
ma , [c] GY
(mn(ASXSIIAXXTT
v VTTO . NT
+ v D + Dra(LS
where 1 [-] is the indicator function, represents node label- ing. The expected margin loss is then defined as
+ v D (PF)
()(()= == Eyy..-
(3)
Definition 1 (Graph-Level Node Heterophily Distribution). Given a graph G, and for any node V, the node-level heterophity is defined as ha(v)= Winj EueN(e) l(Ya # Y.), where (v) denotes the set of neighbors of v. The graph-level heterophily distribution is then defined as the empirical distribution of the random variable ho(v):
where f is the unspecified operator of first-order aggrega- tion, C' is the number of classes, and p, a are constants con- trolled by the node feature distribution of different classes. Proof details and additional analysis are in Appendix A.
How could theory further drive practice? In Theorem reveals four critical factors that may affect the GDA per- formance. (I) (xL x|AT
Pdl (h) = EV ha(v)= = h3ll Ee [0, 1].
represents the graph homophily signal, capturing graph attributes modulated by the adjacency matrix between the source and target graphs. (II) DxL (X (IIT)) represents the divergence in graph at- tribute distributions between the source and target. (III) DRa. (T.S x X²) represents the distribution divergence of graph heterophilc signal between the source and target graphs, where the graph attribute signal is modulated by the graph Laplacian matrix indicating. (IV) DxL (P || P is a fixed intrinsic graph parameter that quantifies the het- erophily distribution shift between the source and target graphs. In other words, to effectively align source and target graphs, one should consider the homophily, attribute, and heterophily signals.
(4)
Here, Pd (h) represents the proportion of nodes in G that have heterophily value of h, forming a probability distri- bution over possible node heterophily values.
For a source domain G and a target domain GT, we de- note their respective graph-level heterophily distribution as PM (h) and PH (h).
Definition 2 Kuullback-eeible Divergence). For continu- ous probability distributions with probability density func- tions p(z) and q(x), the KL divergence is given by:
20 p(x) (_ log p(x)
(pI())))) = Dxi(P1Q)=/
dr.
(5)
g(x))
4. Methology
KL divergence measures the relative entropy or information loss when using Q to approximate P. It is always non- negative, and Dxa (PIlQ) = and only if Q.
Motivated by the aforementioned analysis, our framework needs to capture AX, X and I.X of both source and target

---

Homophily Enhanced Graph Domain Adaptation
is layer-specific trainable weight matrix, a is learnable scalar parameter for the full-pass filtering, H' is the activa- tion matrix in the (-th layer and I!th = X. After applying the full-pass filter to extract attribute information, the output node embedding for the source graph denoted as 2 and output target attribute node embedding is denoted as Z
Source Graph
Hamophilic
Filter
+5+
Source Loss
6
Full--pass
2
Filter
Heterophillo
Homanriik Alganam
fitter
Alignment Lass by
Heterophilic Filter Similarly, we utilize Ии that can cap- ture heterophilic node pattens information. With the input graph G, the 1-th layer's output Hi, can be represented as:
Target Graph
Hoterophilic
Fitter
27
Full-pass Filter
x
H = ReLU (a* -L
(10)
Homophilic
Zip
+2
where HH'''WW' applies heterophilic filtering to the node features from the previous layer H'-1, weight matrix H is a layer-specific trainable weight matrix, a is a learnable scalar parameter for the heterophilic filtering, Hy is the activation matrix in the /-th layer and H = X. After applying the heterophilic filter to extract heterophilic signal, the output node embedding for the source graph is denoted as Z and output target node embedding is denoted Z
Filter
Target Loss
An overview of HGDA. HGDA optimizes heterophily, at- tribute, and homophily graph signals while minimizing homophily distribution shifts between the source and target graphs.
Figure 3.
graph. In practice, we can treat A as homophilc filter and L as heterophilic filter (Nt & Machara, 2019). Thus, as shown in Figure introduce mixed filter to effectively cap- ture information across different homophilic groups while minimizing various levels homophily shift.
4.2. Homophily Alignemnt Loss
The proposed framework follows the transfer learning paradigm, where the model minimizes the divergence of the two graphs. The homophily aligmment method captures and aligns various homophily signals, improving target node classification performance. According to Theorem 7, the dis- crepancy between the source and target graphs is bounded by KL. divergence. To this end, Lu utilizes the KI. diver- gence loss between the source graph embeddings 2 Z and 7 and the target graph zf. 7 and the target graph embeddings Z which can be formulated as:
4.1. Homophily, Full-pass and Heterophily Filter
Homophilic Filter To extract meaningful features from graphs, we utilize H,, that can capture homophile node pattens information. With the input graph G, the (-th layer's output HJ can be represented as:
H = RELU (d-AA''-W?))
(8)
C# - KL ( KL(ZZ + KL(Z
where H - applies homophilic filtering to the node features from the previous layer H/-11 weight matrix Wh-1 is layer-specific trainable weight matrix, a' is learnable scalar parameter for the homophilic filtering, H' is the activation matrix in the I-th layer and H = X. After applying the homophily filter to capture homophile node signal, the output node embedding for the source graph is denoted as zf. Similarly, the output target homophile node embedding denoted as ZT.
(11)
We adapt the embeddings after applying the three filters to enforce graph node aligmment across different homophily ratios. Specifically, K KL(ZÍIIZE) aligns the homophilic signal, corresponding to the term (A* Similarly, KL(Zİ) (ZT) directly aligns the graph at- tributes, corresponding to the term (Xx+ Finally, K [ ( aligns the heterophilic signal, which is con- sistent with the term (L X x x²) in Theorem
Full-pass Filter To obtain comprehensive graph attribute information, we introduce a full-pass filter to extract node attributes. In practice. the full-pass filter is defined as Hp = Ā + f. = J, which is consistent with capturing all attribute information. With the input graph G, the I-th layer's output H. can be represented as:
4.3. Target Node Classification
The source classifier loss L. (Js (79), YS) is to minimize the cross-entropy for the labeled data node in the source domain:
Ns
H' = ReLU (a'-1H' -1H w(-")
(9)
Ls (fs (25) YS) = N₂
Σ y log (i:)
(12)
where
applies full-pass filtering to the node features from the previous layer H'-1, weight matrix W
where z5 = 25 z5. v/ denotes the label of the i-th node the source domain and 0 are the classification
5

---

Homophily Enhanced Graph Domain Adaptation
prediction for the i-th source graph labeled node of E ps:
Paper-Subject-Paeer (PSP) network (Fan al., 2020), while ACM4(A4) is extracted from the ACM2 Paper-Author-PPan Paper (PAP) network (Fu et al., 2020). These datasets inherently differ in their distributions, making them suitable for eval- uating domain adaptation. For a comprehensive overview, refer to Appendix Table 6. We also provide other datasets homophily distibution in Appendix C Figure 7.
To utilize the data in the target domain, we use entropy loss for the target classifier fr:
Nr NT Σ uh log (0?)
Cr (fr
(13)
where n² = -
of' are the classification prediction for the i-th node in the target graph of Finally, by combining LH, Ls, LD and Cr, the overall loss function of our model can be represented as:
5.2. Baselines
We choose some representative methods to compare. GCN (Kipf & Welling, 2016) further solves the efficiency prob- lem by introducing first-order approximation of ChebNet. DANN (Ganin et al., 2016) use 2-layer perceptron to provide features and gradient reverse layer (GRL) to learn node embeddings for domain classification, DANE (Zhang et al., 2019) shared distributions embedded space on differ- ent networks and further aligned them through adversarial learning regularization. UDAGCN (Wu et al., 2020) is dual graph convolutional network component learning framework for unsupervised GDA, which captures knowl- edge from local and global levels to adapt it by adversarial training. ASN (Zhang et al., 2021) use the domain-speciff features in the network to extract the domain- invariant shared features across networks. EGI (Zhu et al., 2021) through Ego-Graph Information maximization to analyze structure-relevaat transferability regarding the difference between source-target graph. GRADE-N (Wu et al., 2023) propose graph subtree discrepancy measure the graph distribution shift between source and target graphs. JHGDA (Shi et al., 2023) explore information from different levels of network hierarchy by hierarchical pooling model. SpecReg (You et al., 2022) achieve improving performance regular- ization inspired by cross-pollinating between the optimal transport DA and graph filter theories. PA (Liu al., 2024c) counter graph structure shift by mitigating condi- tional structure shift and label shift by using edge weights to recalibrate the influence among neighboring nodes. The aforementioned work does not investigate the imppc of homophily distribution shift, which is an essential graph property on GDA.
-= LH + aCs + BCT
(14)
where and 3 are trade-off eters of the framework are updated via backpropagation. A detailed description of our algorithm is provided in Ap- pendix 14.
The param-
5. Experiment
We evaluate three variants of Homophily Alignemnt to un- derstand how its different components deal with the ho- mophilic distribution shift on 5 real-word GDA benchmarks. These variants include HGDA,, which uses only the ho- mophilic filter to obtain and align node embeddings, specif- ically addressing distribution shifts in homophilic groups. Similarly. HGDA, p and HGDAH h only utlize the full-pat full-pass filter and heterophilic filter to obtain and align node em- beddings. The detailed experimental setup can be found in Appendix B.
5.1. Datasets
To demonstrate the effectiveness of our approach do- main adaptation node classification tasks, we evaluate it on four types of datasets, including Airport (Ribeiro et al., 2017), Citation (Wu et al., 2020), Social (Liu et al., 2024a), ACM (Shen et al., 2024), and MAG datasets (Wang et al., 2020). The Airport dataset represents airport networks from three countries and regions: the USA (U), Brazil (B), and Europe (E). In this dataset, nodes correspond airports, and edges denote flight routes. The Citation dataset comprises three citation networks: DBLPv8 (D), ACMv9 (A), and Citationv2 (C), where nodes represent articles and edges indicate citation relationships As for social networks, we choose Twitch gamer networks, which are collected from Germany (DE), England(EN) and FFance(FR). We also use two blog networks, Blog1 (B1) and Blog2 (B2), both tracted from the BlogCatalog dataset. To further evaluate the significance of the homophily distribution effect, we curate a real-world dataset with a significant homophily dis- tribution shift. We utilize two commonly referenced ACM datasets. The dataset ACM3(A3) is derived from the ACM
5.3. Performance Comparison
The results of experiments are summarized in Table 1, Table and Table 3, where highest scores are highlighted in bold, and the aecondhhighes scores are underlined. Some results are directly taken from (Shi al., 2023; Pang al., 2023; Liu et al., 2024b; Zhang et al., 2025). We have the following findings: It can be seen that our proposed method boosts the performance of SOTA methods across most evaluation met- rics on four group datasets, which proves its effectiveness. HGDA outperforms other optimal methods, achieving state- of t--theaatt (SOTA) performance across all datasets. Specifi- cally, HGDA achieves an average improvement of 1.10%
6

---

Homophily Enhanced Graph Domain Adaptation
Methods
U- B
U ->
B +
E
E
E
A3 A4
A4 A3
B1 B2
B2
GCN
0.366
0.371
0.491
0.452
0.439
0.298
0.373
0.323
0,408
0.451
DANN
0.501
0.386
0.402
0.350
0.436
0.538
0.362
0.325
0.409
0,419
DANE
0.531
0.472
0.491
0.489
0.461
0.520
0.392
0.404
0.464
0,423
UDAGCN
0.607
0.488
0.497
0.510
0.434
0.477
0.404
0.380
0.471
0.468
ASN
0,519
0.469
0.498
0.494
0.466
0.595
0.418
0.409
0.732
0.524
EGI
0,523
0,451
0.417
0.454
0.452
0.588
0.511
0,449
0.494
0.516
GRADE-N
0.550
0.457
0.497
0.506
0.463
0.588
0.449
0.461
0.567
0.541
JHGDA
0.695
0.519
0.511
0.569
0.522
0.740
0.516
0.537
0.619
0.643
SpecReg
0.481
0.487
0,513
0,546
0.436
0.527
0.526
0.518
0.661
0.631
0.621
0.547
0.543
0.516
0.506
0.670
0.619
0.610
0.662
0.654
HGDA
0.683
0.709
0.647
HGDA
0.709
0,560
0.541
0.538
0.550
0.691
0.701
0.660
0.665
0.655
HGDA
0.714
0.538
0.524
0.569
0.545
0.690
0.713
0.679
0.656
0.664
HGDA
0.721
0.572
0.569
0.584
0.721
0.718
0.698
0.683
0.677
Table 1. Cross-network node classification on the Airport, ACM and Blog network.
Methods
A D
-> A
C- A
C
D
D -> C
DE
EN
EN -> DE
DE
FR
FR
EN
GCN
0.632
0.578
0.675
0.635
0.666 0.518
0.654
0.523
0.534
0,514
0.568
DANN
0.488
0.436
0.520
0.518
0.465
0.512
0.528
0.581
0.562
DANE
0.664
0.619
0.642
0.653
0.661
0.709
0.642
0.644
0.591
0.574
UDAGCN
0.684
0.623
0.728
0.663
0.712
0.645
0.624
0.660
0,545
0.565
ASN
0.729
0.723
0.752
0.678
0.752
0.754
0,550
0.517
BGI
0.647
0.557
0.676
0.598
0.662
0.652
0.681
0,589
0.537
0.551
GRADE-N
0,701
0.660
0.736
0.687
0.722
0.687
0.749
0.661
0,576
0.565
JHGDA
0.755
0.737
0.814
0.756
0.762
0.794
0.766
0.737
0,590
0.539
SpecReg
0.654
0.727
PA
0.752
0.751
0.804
0.768
0.755
0.780
0.677
0.760
0,521
0.538
HGDA
0.756
0.739
0.794
0.770
0.739
0.757
0.765
0.747
0.532
0.548
HGDA,
0,769
0.747
0.811
0.758
0.759
0.782
0.751
0,749
0,560
0.539
HGDA
0.752
0.738
0.804
0.767
0.761
0.789
0. 0.769
0.751
0,578
0.544
HGDA
0.756
0.787
0.799
0.781
0.763
0.594
Table 2. netsonk node classification on Citation and Twitch network.
Methods
US CN
US DE
US JP
US
RU
US
FR
CN
US
CN
CN
CN
RU
CN
GCN
0.042
0.168
0.219
0.147
0.182
0.193
0.064
0.160
0.069
0.067
DANN
0.242
0.263
0.379
0.218
0.207
0.302
0.134
0.214
0.119
0.107
DANE
0.272
0.250
0,280
0.210
0.186
0.279
0.108
0.228
0.170
0.184
UDAGCN
0OM
0OM
0OM
COM
0OM
COM
0OM
OOM
OOM
0OM
ASN
0.290
0.272
0.291
0.222
0.199
0.268
0.121
0.207
0.189
0.190
OOM
OOM
GRADE-N
0.304
0.299
0.306
0.240
0,217
0.258
0.137
0.210
0.178
0.199
JHGDA
0OM
0OM
0OM
0OM
0OM
OOM
0OM
0OM
0OM
OOM
SpecReg
0.237
0,267
0.377
0,228
0.218
0,317
0.134
0.199
0,109
116
0.400
0.389
0.474
0.371
0,252
0.452
0.262
0.383
0.333
0.242
HGDAz
0,498
0,400
0.314
0.447
0.379
0.418
0.368
0.330
HGDA
0.449
0.457
0,502
0.416
0.329
0,441
0,401
0.395
0,388
0.307
HGDA
0.488
0.468
0.494
0.429
0.330
0.426
0.410
0.411
0.326
0.288
HGDA
0.510
0.497
0,531
0.442
0.347
0.476
0,438
0.435
0.392
0.339
Table Cross-networf node classification on MAG datasets.
on Airport, 6.50% on ACM, 1.40% on Citation, and 2.20% on Blog. Notably, HGDA achieves maximum average im- provement of 8.4 8.49% for ACC on MAG datasets. This illus- trates that our proposed model can effectively aligns varies node homophilic information. Our HGDA variants achieves second-highess than other optimal methods on some of the metrics in various benchmarks. This can be attributed to the varying homophilic pattern distributions across datasets, which are captured by our method's 's variants. For instance,
in the ACM dataset, HGDA, and HGDA generally out- perform HGDAF. indicating that effectively balancing both homophilic and heterophilic information is crucial for this dataset. This observation aligns well with the design of our method. In all cases, HGDA produces better performance than PA (Liu et al., 2024c), which were published 2024. This verifies the advantage of our approach. Our Model efficient experiment be seen in Appendix D

---

Homophily Enhanced Graph Domain Adaptation
(a) UDAGCN
(b) JHGDA
(c) SepeReg
(d) PA
(c) HGDA
Figure 4. Visualizing source and target node embeddings via T-SNE. Each color represents class, while dark and light shades of the same color correspond nodes of the same class from source and target domains, respectively.
5.4. Ablation Study
Among the four variants of HGDA, HGDA performs the best in most cases. HGDAL HGDA,, and HGDA achieve varying performance levels across different groups of datasets, indicating that their effectiveness closely re- lated the node homophilic distribution of the datasets. HGDA is consistently better than all variants, indicating each component boosts the performance. Moreover, we in- vestigate all HGDA variant's classification accuracy across different homophilic subgroup. As shown Figure 5, We observe that HGDA performs well across all subgroups, in- dicating that homophily alignment effectively addresses the shortcomings of GCN in handling various homophily dis- crepancies. In addition, HGDA variants effectively address homophily discrepancies at different levels. Specifically, HGDA performs well in homophilic subgroups, while HGDA excels in heterophilic subgroups, demonstrating the robustness of our model.
828
(a) U E
(b) U B
60
0502
220
2204
66)
(c)
B
R
(d) A4
A3
Figure 5. Classification accuracy of HGDA, HGDAL, HGDAF, and HGDA,, across different subgroups in Airport and ACM
datasets.
5.5. Visualization
In this section, we visualize node embeddings generated by competitive GDA models the task A + D. We observe from Figure Firstly, the nodes belonging to different classes are well-separated from each other. This shows that HGDA is effective in distinguishing between different classes in the embedding space. Secondly, nodes belong- ing to the same class from different domains are mostly overlapping, which indicates that HGDA could significantly reduce domain discrepancy. The first observation indicates good classification, while the latter suggests good domaín alignment.
0.8
Accursoy53
0.74
Accuracy(%)
B
651
8.5
e51
088
A
D
(b) U B
0.7
Accuracy (%)
Accuracy
5.6. Parameter Analysis
0.6
0.5
0.42
05
0.56
0.1
p
In this section, we analyze the sensitivity of hyper- parameters and of our method on Citation, Airport, ACM, and MAG datasets. First, test the performance with different and 8. As shown in Figure 6, HGDA has competitive performance suggests the stability of our method. For a more detailed
0.91
008
(c) A4
A3
(d) US +
CN
large range of values, which
Figure 6. The influence of parameters and 8 on Citation, Airport, ACM and MAG datasets.
8

---

Homophily Enhanced Graph Domain Adaptation
analysis and result, refer to the Appendix E.
transfer learning via adversarial domain adaptation with graph convolution. IEEE Transactions Knowledge and Data Engineering, 35(5):4908-49222 2022.
6. Conclusion
In this paper, we propose HGDA framework to solve the GDA problem in cross-network node classification tasks. We reveal the importance of the homophily shift in GDA through both empirical and theoretical analysis. Our ap- proach minimizes homophily distribution shifts by optimiz- ing homophilic, heterophilic, and attribute signals. Compre- hensive experiments verify the superiority of our approach. We will also delve deeper into graph domain adaptation theory to develop more powerful models by considering different architectures (Zhuo al., 2023; 2024a; Yang et al., 2025; 2024b).
Fan, S., Wang, X., Shi, C.,, Lu, E.., Lin, K., and Wang, B. One2multi graph autoencoder for multi-view graph clustering. In proceedings of the web conference 2020, pp. 3070-3076, 2020.
Fang, R.. Wen, L., Kang, Z., and Liu, J. Structure-preeett preserving graph representation learning. In 2022 IEEE Interna- tional Conference on Data Mining (ICDM), pp. 927-932. IEEE, 2022.
Fang, R., Li, B., Kang, Z.,, Zeng, Q. Dashthayaz, N. H., Pu, R., Wang, B., and Ling, C. On the benefits of attribute- driven graph domain adaptation. In The Thirteenth Inter- national Conference Learning Representations, 2025.
Acknowledgments
This work is supported by the Natural Sciences and Engi- neering Research Council of Canada (NSERC) Discovery Grants program.
Fu, X., Zhang, J., Meng, Z., and King. Magnn: Metapath aggregated graph neural network for heterogeneous graph embedding. In Proceedings of the web conference 2020, pp. 2331-2341 2020.
Impact Statement
Ganin, Y., Ustinova, E.,, Ajakan, H., Germain, P., Larochelle, H., Laviolette, F., March, M., and Lempitsky, V. Domain- adversarial training of neural networks. Journal of ma- chine learning research, 1 2016.
This paper presents work whose goal is to advance the field of Machine Learning. There are many potential societal consequences of our work, none which we feel must be specifically highlighted here.
Guo, G., Wang, C., Yan, B., Lou, Y., Feng, H., Zhu, J., Chen, J., He, F., and Yu, P. Learning adaptive node embeddings across graphs. IEEE Transactions on Knowledge and Data Engineering, 2022.
References
Bobkov, S. G. and Götze, F. Exponential integrability and transportation cost related to logarithmic sobolev inequal- ities. Journal of Functional Analysis, 163(1):1-28, 1999.
He, X., Wang. Y., Fan, W., Shen, X., Juan, X., Miao, R., and Wang, X. Mamba- based graph convolutional networks: Tackling over-smoothing with selective state space. arXiv preprint 2rXiv:2501.55461 2025.
Chen, M., Wei, Z., Huang, Z., Ding, B., and Li, Y. Sim- ple and deep graph convolutional networks. In Interna- tional Conference on Machine Learning, pp. 1725-1735. PMLR, 2020.
Huang. Du, L., Chen, X., Fu, Q., Han, S., and Zhang, D. Robust mid-pass filtering graph convolutional networks. In Proceedings of the ACM Web Conference 2023, pp. 328-338 2023.
Chen, Y., Song, S., Li, S., and Wu, C. A graph embed- ding framework for maximum mean discrepancy-based domain adaptation algorithms. IEEE Transactions on Image Processing, 19:199-213, 213,211, 2019.
Huang, J., Shen, J.. Shi, X., and Zhu, X. On which nodes does gen fail? enhancing gen from the node perspec- tive. In Forty-first International Conference on Machine Learning, 2024.
Chen, Z., Mao, H., Liu, J., Song, Y., Li, B., Jin, W., Fatemi, B., Tsitsulin, A., Perozzi, B., Liu, H., et al. Text-space graph foundation models: Comprehensive benchmarks and new insights. arXiv preprint arXiv:2406. 10727, 2024.
Kang, Z., Xie, X., Li, B., and Pan, E. Cdc: simple frame- work for complex data clustering. IEEE Transactions on Neural Networks and Learning Systems, 2024.
Chien, E., Peng, J., Li, P., and Milenkovic, O. Adaptive uni- versal generalized pagerank graph neural network. In 9th International Conference on Learning Representations, ICLR 2021,, 2021.
Kingma, D. P. and Ba, J. Adam: A method for stochastic optimization. In International Conference on Learning Representations (ICLR), 2015.
Dai, Q., Wu, X.M.., Xiao, J., Shen, X., and Wang, Graph

---

Homophily Enhanced Graph Domain Adaptation
Kipf, T. N. and Welling, M. Semi-supervised classifica- tion with graph convolutional networks. arXiv preprint arXiv: 1609. 02907, 2016.
Liu, M., Zhang, Z., Tang, J., Bu, J., He, B., and Zhou, S. Re- visiting, benchmarking and understanding unsupervised graph domain adaptation. NeurIPS 2024 Track Datasets and Benchmarks, 2024b.
Li, B., Pan, E., and Kang, Z. Pc-conv: Unifying homophily and heterophily with two-fold filtering. In Proceedings of the AAAI conference on artificial intelligence, volume 38, pp. 13437-13444 1344, 2024a.
Liu, S., Zou, D.. Zhao, H., and Li, Pairwise align- ment improves graph domain adaptation. arXiv preprint arXiv:2403.011 000900092 2024c.
Li, B., Chen, Z., Han, H., Zeng, S., Liu, J., and Tang, J. Unveiling mode connectivity in graph neural networks. arXiv preprint 2rX.v:2502. /2008, 2025a.
Luan, S., Hua, C., Lu, Q. Zhu, J., Zhao, M., Zhang. S., Chang, X.-W,, and Precup, D. Revisiting heterophily for graph neural networks. Advances in neural information processing systems, 25:1362-1375 2022.
Li, B., Xie, X., Lei, H., Fang, R., and Kang, Z. Simplified penet with robustness. Neural Networks, 184:197099, 2025b.
Ma, J., Deng. J., and Mei, Q. Subgroup generalization and fairness of graph neural networks. Advances Neural Information Processing Systems, 34: 1048-1061, 2021.
Li, H., Wang, W., Wang, Luo, Z., Liu, X., Li, K., and Cao, X. Phrase grounding-based style transfer for single- domain generalized object detection. arXiv preprint arXiv:2402.011 304, 2024b.
Mao, H., Chen, Z., Jin, W., Han, H., Ma, Y., Zhao, T., Shah, N., and Tang, J. Demystifying structural disparity in graph neural networks: Can one size fit all? Advances in neural information processing systems, 36, 2024a.
Li, H., Yang, X., Wang, M., Lam, L., Liang, Liu, X., and Li, K. Object style diffusion for generalized object de- tection in urban scene. arXiv preprint 188555 2024c.
Mao, H., Du, L.,, Zheng, Y., Fu, Q.. Li, Chen, X., Han, S., and Zhang, D. Source free unsupervised graph domain adaptation. The 17th ACM International Conference on Web Search and Data Mining, 2024b.
Li, H., Xiao, Y., Liang, K., Wang, M., Lan, L., Li, K., and Liu, X. Let synthetic data shine: Domain reassembly and soft-fusion for single domain generalization. arXiv preprint arXiv:2503. 13617, 2025c.
Miao, R., Zhou, K. Wang, Y., Liu, N., Wang, Y., and Wang, X. Rethinking independent cross-entropy loss for graph- structured data. In Forty-first International Conference on Machine Learning. ICML 2024, Vienna, Austria, July 21-27, 2024. OpenReview.net, 2024. URL https: openreview net forum? fid=:rdd=drieee 9MQQN.
Li, X., Zhu, R., Cheng, Y., Shan, C., Luo, S., Li, D., and Qian, W. Finding global homophily in graph neural net- works when meeting heterophily. In International Con- ference Machine Leurning, ICML 2022, volume 162, pp. 13242-13256. PMLR, 2022a.
Nt, H. and Machara, T. Revisiting graph neural net- works: All we have low-pass filters. arXiv preprint arXiv: 0005/99050000 9955009550, 2019.
Li, X., Zhu, R., Cheng, Y., Shan, C., Luo, S., Li, D., and Qian, W. Finding global homophily in graph neural net- works when meeting heterophily. In International Con- ference Machine Learning, 2022b.
Pang. J., Wang. Z., Tang. J., Xiao, M., and Yin, N. Sa-gda: Spectral augmentation for graph domain adaptation. In Proceedings of the 31 ACM international conference on multimedia, pp. 309-318. 2023.
Lim, D., Li, X., Hohne, F., and Lim, S.-N. New benchmarks for learning non-homone non-homophilous graphs. International World Wide Web Conferences, 2021.
Pei, H., Wei, B., Chang, K. C.-C., Lei, Y., and Yang, B. Geom-gen Geometric graph convolutional networks. In International Conference on Learning Representations.
Liu, J., Hua, Z. Xie, Y., Li. B., Shomer, H., Song, Y., Hassani, K., and Tang, J. Higher-order structure boosts link prediction on temporal graphs. arXiv preprint TrXiv:2505.15746 2025.
Pu, R., Xu, G., Fang, R., Bao, B.-K., Ling, C., and Wang, B. Leveraging group classification with descending soft labeling for deep imbalanced regression. Proceed- ings of the AAAI Conference on Artificial Intelligence, volume 39, pp. 19985, 2025.
Liu, M., Fang, Z., Zhang, Z., Gu, M., Zhou, S., Wang, X., and Bu, J. Rethinking propagation for unsupervised graph domain adaptation. In Proceedings of the AAAI Confer- ence on Artificial Intelligence, volume 38, pp. 13963- 13971, 2024a.
Qian, X., Li, B., and Kang. Z. Upper bounding barlow twins: novel filter for multi-relational clustering. In Proceedings of the AAAI conference on artificial intelli- gence, volume 38, pp. 14660-1 14668, 2024.
10

---

Homophily Enhanced Graph Domain Adaptation
Qiao, Z., Luo, X., Xiao, M., Dong, H., Zhou, Y., and Xiong, H. Semi-supervised domain adaptation in graph transfer learning. IJCAI, 2023.
Xie, X., Pan, E., Kang, Z., Chen, W., and Li, B. Prov- able filter for real-world graph clustering. arXiv preprint arXiv:2400 243.::4003.3666,, 2024.
Ribeiro, L. F., Saverese, P. H., and Figuciredo, D. R. struc2vec: Learning node representations from structural identity. In Proceedings of the 23rd ACM SIGKDD in- ternational conference on knowledge discovery and data mining, pp. 385-394, 2017.
Xic, X., Li, B.. Pan, E., Guo. Z., Kang, Z., and Chen, W. One node one model: Featuring the missing-half for graph clustering. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 39, pp. 21 21688-216999 2025.
Shen, X. and Chung, I.. Network embedding for cross-network node classification. arXiv preprint arXiv: 072644, 2019.
Xu, G., Chen, Q. Ling, C., Wang, B., and Shui, C. Intersectional unfairness discovery. arXiv preprint arXi::405..0790, 2024a.
Shen, X., Dai, Q. Chung, F.-I,, Lu, W., and Choi, K.-S. Adversarial deep network embedding for cross-network node classification. In Proceedings of the AAAI confer- ence artificial intelligence, volume 34, pp. 2991-2999, 2020a.
Xu, G., Guo, H., Yi, L., Ling. C., Wang, B., and Yi, G. Re- visiting source- free domain adaptation: a new perspective via uncertainty control. In The Thirteenth International Conference on Learning Representations, 2024b.
Xu, G., Yi, L., Xu, P., Li, J., Pu, R., Shui, C., Ling, C., McLeod, A. I., and Wang, B. Unraveling the mysteries of label noise in source- free domain adaptation: Theory and practice. IEEE Transactions on Puttern Analysis and Machine Intelligence, 2025.
Shen, X., Dai, Q. Mao, S., Chung, F.-1., and Choi, K.-.. Network together: Node classification via cross-network deep network embedding. IEEE Transactions on Neu- ral Networks and Learning Systems, 1235)11935, 2020b.
Xu, Z., He, H., Lee, G.-H,, Wang, Y., and Wang, H. Graph-relational domain adaptation. arXiv preprint Stti:22002036226 2022.
Shen, X., Pan, S., Choi, K.-.,, and Zhou, X. Domain- adaptive message passing graph neural network. Neural Networks, 164:439-454, 2023.
Yan, B. and Wang, C. Graphae: adaptive embedding across graphs. In 2020 IEEE 36th International Conference on Data Engineering (ICDE), pp. 1958-1961. IEEE, 2020.
Shen, Z., He, H., and Kang, Z. Balanced multi-relational graph clustering. In Proceedings of the 32nd ACM In- ternational Conference on Multimedia, pp. 4120 4128, 2024.
Yang, L., Li, M., Liu, L., Niu, B., Wang, C.,, Cao, X., and Guo, Y. Diverse message passing for attribute with het- erophily. In Advances in Neural Information Processing Systems 34, NeurlPS 2021,, pp. 4751-4763, 2021.
Shi, B., Wang, Y., Guo, F., Shao, J., Shen, H., and Cheng, X. Improving graph domain adaptation with network hierarchy. In Proceedings of the 32nd ACM International Conference on Information and Knowledge Management, pp. 2249-2258, 2023.
Yang, L., Li, Z., Zhuo, J., Liu, J., Ma, Z., Wang, C., Wang, Z., and Cao, X. Graph contrastive learning with joint spectral augmentation of attribute and topology. In AAAI, pp. 19983921991, 2025.
Shi, B., Wang, Y., Guo, F., Xu, B., Shen, H., and Cheng, X. Graph domain adaptation: Challenges, progress and prospects. arXiv preprint arXiv.2402.00904 2024.
Yang, X., Liu, Y., Zhou, S., Wang, S., Tu, W., Zheng, Q.. Liu, X., Fang, L., and Zhu, E. Cluster Cluster-guided contrastive graph clustering network. In Proceedings of the AAAI con- ference on artificial intelligence, volume 37, pp. 10834- 10842, 2023a.
Wang, K. Shen, Z., Huang, C., Wu, C.-H., Dong, Y., and Kanakia, A. Microsoft academic graph: When experts are not enough. Quantitative Science Studies, 1(1):396 413, 2020.
Yang, X., Tan, C., Liu, Y., Liang, K., Wang, S., Zhou, S., Xia, J., Li, S. Z., Liu, X., and Zhu, E. Convert: Contrastive graph clustering with reliable augmentation. In Proceedings of the 3/ ACM International Conference on Multimedia, pp. 319-327, 2023b.
Wu, J., He, J.. and Ainsworth, E. Non-iid transfer learn- ing on graphs. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 37, pp. 10342-10350, 2023.
Wu, M.. Pan, S., Zhou, C., Chang, X., and Zhu, X. Unsu- pervised domain adaptive graph convolutional networks. In Proceedings of The Web Conference 2020, pp. 1457- 1467, 2020.
Yang, X., Min, E., LIANG, K., Liu, Y., Wang, S., Wu, H., Liu, X., Zhu, E., et al. Graphlearner: Graph node clustering with fully learnable augmentation. In ACM Multimedia 2024, 2024a.

---

Homophily Enhanced Graph Domain Adaptation
Yang, X., Wang, Y., Liu, Y., Wen, Y., Meng, L.,, Zhou, S., Liu, X., and Zhu, E. Mixed graph contrastive network for semi-supervised node classification. ACM Transactions on Knowledge Discovery from Data, 2024b.
Zhu, Q., Yang, Xu, Y., Wang, H., Zhang, C., and Han, J. Transfer learning of graph neural networks with ego- graph information maximization. Advances in Neural Information Processing Systems, 34:1766- 1779, 2021.
You, Y., Chen, T., Wang, 7.., and Shen, Y. Graph domain adaptation via sncory-grounded spectral regularization. In The Eleventh International Conference on Learning Representations, 2022.
Zhuo, J., Cui, C., Fu, K., Niu, B., He, D., Guo, Y., Wang. Z.. Wang, C.,, Cao, X., and Yang, L.. Propagation all you need: A new framework for representation learning and classifier training on graphs. In MM, pp. 481-489, 2023.
Zhuo, J., Cui, C., Fu, K., Niu, B., He, D., Wang, C., Guo, Y., Wang, Z., Cao, X., and Yang, L. Graph contrastive learning reimagined: Exploring universality. In WWW, pp. 641-651, 2024a.
Yuan, J., Luo, X., Qin, Y., Mao, Z., Ju, W., and Zhang, M. Alex: Towards effective graph transfer learning with noisy labels. In Proceedings of the 31st ACM Interna- fional Conference on Multimedia, pp. 3647-3656, 2023.
Zhuo, J., Lu, Y., Ning, H., Fu, K., Niu, B., He, D., Wang, C., Guo, Y., Wang, Z., Cao, X., and Yang, L. Unified graph augmentations for generalized contrastive learning on graphs. In NeurlPS, 2024b.
Zeng, Q. Wang, W., Zhou, F., Ling, C., and Wang, B. Fore- see what you will learn: data augmentation for domain generalization in non-stationary environment. In Pro- ceedings of the AAAI conference on artificial intelligence, volume 37, pp. 11147-11155, 2023.
Zhuo, J., Qin, F., Cui. C., Fu, K., Niu, B., Wang, M., Guo, Y., Wang, C., Wang, Z., Cao, X., and Yang, L. Improving graph contrastive learning via adaptive positive sampling. In CVPR, pp. 23179-23187, 2024c.
Zeng. Q., Wang. W., Zhou, F., Xu, G., Pu, R., Shui, C.,, Gagné, C., Yang, S., Ling, C. X., and Wang, B. General- izing across temporal domains with koopman operators. In Proceedings of the AAAI Conference on Artificial In- telligence, volume 38, pp. 16651-16659, 2024.
Zhuo, J., Liu, Y., Lu, Y., Ma, Z., Fu, K., Wang, C., Guo, Y., Wang. Z., Cao, X., and Yang, L. Dualformer: Dual graph transformer. In ICLR, 2025.
Zeng, Q. Huang, J., Lu, P., Xu, G., Chen, B., Ling, C., and Wang, B. Zeta: Leveraging z-order curves for efficient top-k attention. ICLR, 2025.
Zhang, X., Du, Y., Xie, R., and Wang, C. Adversarial separation network for cross-newt cross-network node classification. In Proceedings of the 30th ACM International Conference on Information & Knowledge Management, pp. 2618- 2626, 2021.
Zhang, Y., Song, G., Du, L., Yang, S., and Jin, Y. Dane: Domain adaptive network embedding. arXiv preprint arXiv:1906.0066: 00684, 2019.
Zhang, Z., Liu, M., and He, B. Pygda: A python li- brary for graph domain adaptation. arXiv preprint arXiv:2503.10284, 2025.
Zhu, J., Yan, Y., Zhao, L., Heimann, M., Akoglu, L., and Koutra, D. Beyond homophily in graph neural networks: Current limitations and effective designs. Advances in Neural Information Processing Systems, 33:7793-7804, 2020a.
Zhu, J., Yan, Y., Zhao, I.., Heimann, M., Akoglu, L., and Koutra, D. Beyond homophily in graph neural networks: Current limitations and effective designs. Advances in neural information processing systems, 33:7793-7804, 2020b.
12

---

Homophily Enhanced Graph Domain Adaptation
A. Proof
Definition (I-Wasserstein Distance of Node Heterophily Distributions), Let G (V,8,A,X,Y) and G' (V','', A',''''', X', (Y)" be two graphs with node heterophily distributions:
hig Pv, ha Pv.
(15)
We define their 1- I-Wasserstein Distance as:
Wi Viaha, har)
inf ren(Py,Pe)
BanN) MI].
(16)
where:
[I([v, denotes the set of all joint distributions r(h, whose marginal distributions are Pv and Pv., respectively,
This distance measures the minimum transportation cost required to transform the distribution Py into Pv., where the transportation cost is given by hh h!).
This metric characterizes the optimal transport distance between the node heterophity distributions of two graphs and enables the comparison of their overall heterophily structures. Specifically:
If har) Ri O, the graphs have very similar heterophily distributions.
WfG, h ( is large, the heterophily structures of the two graphs are significantly different.
Corollary 2 (Wasserstein-1 Distance for Feature Distributions), Let P5 and Pf be the empirical distributions of node features f in the source graph GS and target graph GT, respectively. The I-Wasserstein distance between these distributions given by:
inf B [l] fl. W1(P5 Pf) -FFEI((P .F)
(17)
where IT(E Pf) is the set of all joint distributions -F(( with marginals P5 and Pf. This measures the minimum transportation cost required to transform the feature distribution of G into that of GT.
Corollary (Wasserstein-I 1 Distance for Node Heterophily Distributions). Let P and Pf be the empirical distributions of node heterophily values in the source graph G and target graph GT, respectively. The I-Wasserstein distance between these distributions is given by:
Wi PH)
inf ""EM[p PH)
B( hyl],
(18)
where I[(P ,PH) is the set of all joint distributions " (1. with marginals P and P This quantifies the minimum transportation cost to align the heterophily distribution between the two graphs.
Lemma (Upper Bound on Wassersttei Distance via KL Divergence). (Bobkov & Götze, 1999) Let P and Q be two probability distributions on metric space (X.d), where P < Q (i.e., is absolutely continuous with respect to Q). Assume that:
X has bounded support with diameter D, i.e., d(x,y) S D for all x, E X.
There exists constant Co > 0 such that all 1 finintchitrfuunctioos f X + R satisfy the concentration inequality:
sup
E P
[x)))(())) S
(19)
JEFL
Then, the J-Wasserstein distance satisfies the following upper bound:
(P Q) S Cov Dka(PIlQ)
(20)
The constant C depends on the geometry of the space X and the metric d.
13

---

Homophily Enhanced Graph Domain Adaptation
Definition (Expected Loss Discrepancy). Given distribution P over a function family H. for any À > 0 and 7 for any G and GT,, define the expected loss discrepancy between ys and V as (P: == In Reg pe > (0)-
where C (Ø) and (o( follow the definition of Eq. (3).
Lemma 2 (Adaptation from (Ma et al., 2021)). Let + be a family of classification functions. For any classifier á in 2, and for any parameters X > 0 and 2 O, consider any prior distribution P over & that is independent of the training data vs. With a probability of at least 1 over the sample Y x²,for any distribution Q on & such that Pra-Q [max;EvSurT ((x((X (,,,G)))_(((C_C_.___ (ello < <gl > 2' the following inequality holds:
X²
+ DDS.((P:)) (2) S Cz(0) + À (QI))) 8 4No
+
Proposition 1 (Bound for T (P; Adaptation from (Ma et al., 2021: Mao et al.. 2024a; Fang et al., 2025)). For any y 2 O, and under the assumption that the prior distribution P over the classification function family &b is defined, we establish bound for the domain discrepancy measure D (P;A), Specifically, have the following inequality:
(P:A)
1
Σ
In3 +
ApC
(1If - Sall + 114 h11--11 .))
max max(Ns,
NT
V2To
iEVs
JEV,
ApC
WW(PP PF) + W1(P5' P
(21)
V2Ta .s..NN Nr ApCCo
Daa (PF)) DRL (1
V2TO Ng Nr
where f is the unspecified operator of first-order aggregation consideriig f AX and f = LX two easy cases), C the number of classes, and p. are constants controlled by the node feature distribution of different classes.
Proof. We will prove the proposition by establishing the two key inequalities in the given equation.
Proof of the First Inequality (Using Prior Works):
From the cited works (Ma al., 2021; Mao al., 2024a; Fang al., 2025), it follows that the expected loss discrepancy measure D A) can be bounded by:
(PP()) max NT) SEVS
In3 +
V2TO (II - fill + 1/+ h11 0)
ACp
(22)
NT
JEV
This follows from existing domain adaptation literature, where the domain discrepancy measure be controlled by sum over pairwise differences of node features and heterophily values.
Proof of the Second Inequality:
We now show that:
In3 + ACp
(llf: fyll + 1h, - h44 h-sh-p)) p) -p)
(23)
Max(NN, NT)
NT JEVT
V2To
VEV3
XCp
(Wi Pf) + p (PH PH))
(24)
V2TO- .Ng
NT
From Corollary 2, we know that the Wasserstein-1 distance between the node feature distributions is:
inf B( [1 f]]]--
(25)
FFETPP PMPPP.P. pf)
Since the sum over all node pairs approximates an expectation over joint coupling of the distributions, we approximate:
Σ ΣΣ
lI f,l Wi PF).
(26)
iEV: JEV,
14

---

Homophily Enhanced Graph Domain Adaptation
Substituting this into our sum, we obtain:
ΣΣ I1, fyll NsW Pf). NT
(27)
KeVs JEVT
Similarly, from Corollary 3, we have:
Wi(PS p
inf
[1h - -hyll
(28)
y " ppppy pP)
Following the same argument as before, we approximate:
E
Σ JEV
h4 hy] = NsNTWW(PS. )P)).
(29)
Thus:
h4 - ΣEN
ΣE NT
(30)
iEVss JEVT
Now substituting these bounds into our sum:
ΣΣ JEV
In3 +
ACp
(1Ib fill + 11: N1l
.p) p)
(31)
V2TO
JEVT
ACP Ns(Wi Pf) pW: PW PH))
Σ
h3+
(32)
2
VEV3 JEVT
Dividing by max(Ns, NT), we obtain:
1
Σ
Σ
In +
ACp (1ls fyll + 114 - h12 p)
(33)
max(Ns, NT)
V2T0
REVo JEVr JEV
ACp
(Wi(P5 Pf) pW₂ (P Pf))
(34)
2TT Ns NT
Proof of the Third Inequality:
From Lemma (Bobkov-Götze Inequality) (Bobkov & Götze, 1999), we have:
Wi(PS, ,f) S Co (KL(P5) PF),
(35)
W1PPH,PH & Cov PPL(PH||P
(36)
Using these bounds in:
ApC
WWiPPS PF) + PW1 PP")
(37)
V2TO Ng Nyr
we obtain:
XpCCo
[VDaLPPileff (1F + V
(38)
V2Ta -N..N -r
Combining both inequalities, establish the bound:
ApCCo
(DDL(P)(PPF) + (PH(P)
D (P:A)) V2na Ns. NNr
(39)
This completes the proof.
15

---

Homophily Enhanced Graph Domain Adaptation
Corollary (KL Divergence Decomposition of Feature Distributions). Let PS and Pf be the feature distributions in the source and larget domains, respectively. Suppose that node features X undergo transformations defined by the adjacency matrix A and Laplacian matrix L, i.e.,
Pg P(ASX5 19X91X9)P(X9), = P L XX
(40)
Then, the KI. divergence between the feature distributions satisfies:
DEL (PF)) S ( + DKL(XX +
(41)
Proof. Using the chain rule for KL divergence, we decompose:
DEL - XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
DRL
(42)
Applying the chain rule:
DKL (P51PP)) = DxI, (x((((()))P(x))) + (P(A5 I , x'x*
(43)
Assuming conditional independence between adjacency and Laplacian transformations:
DKL
S D (A (A + DKL (L
(44)
Thus, combining the results:
Dxx(X DRL (P (F51) DRL (A (xxx))))) Dx.((5X(11LXXT))
(45)
This completes the proof.
Lemma 3. [Domain Adaptation Bound for Deterministic Classifters] Let & be a family of classification functions. For any classifier o in T, and for any parameters À 0 and O, consider any prior distribution P over t that is independent of the training data Vs. With probability of at least 1 5 over the sample Y for any distribution Q on & such that the following inequality holds:
S 5 + ((1))
+
(46)
+ 4Ns + (P;A)
(47)
Theorem 5. Let & be a family of classification functions. For any classifier 4, and for any parameters X 0 and 7 O. consider any prior distribution P over & that is independent of the training data VS. With probability least 1 - 8 over the sample S for any distribution Q on & we have:
(0) 2 Zg( + (QPP) +
A
+ ApCCo
4Ns
V2TO Ng. -oT
(48)
[ Dx.((AX9 + (X + / (ra(ISXS(IIIXT) + (MM(PP(1PP
Proof. By Lemma 3, the domain adaptation bound is given by:
x 1 2 2(Dk) 1) In 8
1
+
A
+ (P:
(49)
4Ns
From Proposition 1, we substitute the bound on D3/22
XpCCo
(P:A( V2TO Ng. Nr
DKa(PF) + v (PM
(50)
16

---

Homophily Enhanced Graph Domain Adaptation
Applying Corollary 4 to decompose D (P5 Pf), obtain:
(RL [PF)) < DKL (A X I|Axx") ( DxL(X*
+ +
(51)
Similarly, for the heterophily-boe KL divergence:
DKL (IPP) & X' + DKL(X)I
+ ( +xx((Xx((IX
(52)
Thus, we obtain:
D 22/2 (P;A)
ApCCo 2TTO Ns- Nr
+ Dx((SXX (A + +
(53)
Substituting this into the original bound for CP(0), , we conclude:
A
(7(0) - [g(d)
x 2 21 (UIi(
+1
4No
(54)
V Ns Nr [D + DRu(X+|IXT)+ / (
ApCCa
This completes the proof.
B. Experimental Setup
The experiments are implemented in the PyTorch platform using an Intel(R) Xeon(R) Silver 4210R CPU @ 2.40GHz, and GeForce RTX A5000 24G GPU. Technically, two layers GCN is built and we train model by utilizing the Adam (Kingma & Ba, 20155 optimizer with learning rate ranging from 0.0001 to 0.0005. In order to prevent over-fitting, we set the dropout rate to 0.5. In addition, we set weight decay E {le 4, ... 5c 3}. For faimess, we use the same parameter settings for all the cross-domain node classification methods in our experiment, except for some special cases. For GCN, UDA-GCN, and JHGDA the GCNs both the source and target networks contain two hidden layers (L = 2) with structure as 128 16. The dropout rate for each GCN layer set 0.3. We repeatedly train and test our model for five times with the same partition of dataset and then report the average of ACC.
CN
Citationv1
Blog1
DBLPv7
Blog2
Density
Density
ACMv3
Dersity
2
Density
FR
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50 Hiude
0.75
1.00
Hyade
Hinde
Havee
(a) MAG
(b) Citation
(c) Blog
(d) Twitch
Figure 7. This shows local node homophily distibution shift is existing MAG, Citation, Blog and Twitch datasets.
C. Empirical Study: Homophily Divergence Effect to Target classification Performance
In this appendix, we extend our analysis by presenting the homophily distributions and performance results for additional datasets, including Blog, Citation, Twitch, and MAG. As shown in Figure 7, these datasets exhibit clear shifts in homophily distributions between the source and target graphs, further underlining the necessity of our proposed GDA method. The experiments focus assessing the impact of homophily divergence target node classification performance. Using standard two-layer GCN with unsupervised GDA settings, we evaluated classification accuracy across varying homophily ratio subgroups. The following detail observations are drawn from the analysis:
Homophily Distribution Differences: Similar to the Airport dataset discussed the main text, the Blog, Citation, Twitch, and MAG datasets show significant divergence in homophily ratios between the source and target graphs. These shifts result in node subgroups with varying levels of homophilic and heterophilic groups, as illustrated Figure 7.
17

---

Homophily Enhanced Graph Domain Adaptation
Aecoet DnTerwo
CN
Pesert Dileece
Puraet DPharncc
11
O
D1 -13
F-CM
-U-
012.5
20
ane
daed
2403
(a) CN + FR
(b) CN + US
(c) JP
(d) CN +
Perart Offorent
Fecus: D Parers
Pouet STeee
Oan buste Ciargenok
US
US
R1-15
US 1--13
Hemoot Distoeaoo
Hemoo
6203
asel
620)
dses
US + FR
(f) US DE
US RU
(h) US JP
Bocert Bifeernce
Poirert Eiferrae
Peccei Pireere
Dk
80
-1
00
Recarbty ml
nast
soal
DE +
EN
DE
FR
(k) EN
+
FR
B1
B2
Figure 8. GCN performance cross-network classification tasks across different homophily ratio ranges for the MAG, Twitch, and Blog datasets.
18

---

Homophily Enhanced Graph Domain Adaptation
Dataset
Method
Training Time (Normalized wat. UDAGCN)
Memory Usage (Normalized W.L. UDAGCN)
Accuracy(7)
UDAGCN
1
0.607
JHGDA
1.314
1.444
PA
0.498
0.517
0,481
SpeeReg
0.463
0.493
0.621
HGDA
0.514
0.314
0.721
UDAGCN
0,472
JHGDA
1.423
1.513
0.519
U-+B
0.511
0.509
0.547
SpecReg
0.517
0.503
0.487
HGDA
0.307
0.310
0.572
UDAGCN
JHGDA
1,311
1.501
0.569
PA
0.502
0.497
0,516
B-E
SpecReg
0,407
0.503
0.546
HGDA
0.309
0.313
0.584
UDAGCN
1 1.501
0,510
JHGDA
1.311
0.569
PA
0,502
0.497
0.562
A-D
SpecReg
HGDA
0.309
0.313
0.791
UDAGCN
1 1.501
0,510
JHGDA
1,311
PA
0,502
0.497
0,562
SpecReg
0.407
0.503
0.536
HGDA
0.309
0.313
0.326
UDAGCN
0,510
JHGDA
1.311
1,501
0.570
0.502
0.497
C-D
SpecReg
0.407
0.503
0,536
HGDA
0.309
0,313
0.326
Table 4. Comparison of Training Time, Memory Usage, and Accuracy Airport datset.
Impact on Classification Accuracy: we use a two-layer GCN with standard unsupervised GDA settings as our evaluation model. After completing model training, we report the classification accuracy for different homophily ratio subgroups. In the figure, the x-axis represents different node subgroups, where each subgroup consists of nodes within specified homophily ratios range. The left y-axis denotes the proportion of nodes in the entire graph, while the upper-right y-axis shows the percentage difference in homophily ratios between the source and target graphs for each subgroup. The lower-right y-axis indicates the GDA node classification accuracy the target graph for each subgroup. As shown in Figure 8, classification accuracy on the target graph depends on the proportion difference of nodes belonging to subgroups with varying homophily ratios. The figure illustrates that subgroups with lower homophily ratio differences achieve better classification performance, while those that deviate more from the source graph tend to exhibit lower accuracy. Experimental results reveal a negative correlation between homophily divergence and GDA performance. More significant disparities homophily ratios between the source and target graphs lead to lower classification accuracy on the target graph. This trend underscores the importance of GDA in accounting for homophily discrepancies across domains.
D. Model Efficient Experiment
Model Complexity: Here, we analyze the computational complexity the proposed HGDA. The computational complexity primarily depends on the three filter layers. For a given graph G, let N represent the total number nodes in the graph and
the feature dimension. For the three filters: Homophilic Filter Hy; Includes matrix multiplication with W (O(N2 d)) Heterophilic Filter H:: O(v2.... d). Full-pass Filter H O d). Thus, the total complexity of HGDA is: O(N2 d). Since HGDA does not introduce complex modules, its model complexity remains low, comparable that of MLP GCN.
Model Efficient Experiment: To further evaluate the efficiency of HGDA, Table 4 presents running time comparison across various algorithms. We also compared the GPU memory usage of common baselines, including UDAGCN and the recent state-of-the-as methods JHGDA, PA, and SpecReg, which align graph domain discrepancies through different ways. As shown in Table, the evaluation results on airport and citation dataset further demonstrate that our method achieves superior performance with tolerable computational and storage overhead.
19

---

Homophily Enhanced Graph Domain Adaptation
E. Parameter Analysis
The effectiveness of Graph Domain Adaptation (GDA) is highly influenced by the homophily distribution differences between the source and target graphs. Homophily ratios, defined as the likelihood of connected nodes sharing similar attributes or labels, play a crucial role in determining how well embeddings align across domains. To address these variations, the hyperparameters a and & are selected from the set {0.01, 0.05, 0.1, 0.5, 1), providing flexibility in balancing the contributions of source label supervision, domain alignment, and target graph adaptation.
The Airport dataset represents transportation networks, typically characterized by a smaller number of nodes with complex edge relationships and sparse connectivity. The homophily ratio in this dataset is relatively low, which highlights the importance of capturing key node alignment information and homophilic relationships to maintain meaningful structure. The sparsity of connections and low homophily ratios require higher and 3 values to emphasize alignment between source and target graphs. This ensures that even sparse but critical homophilic relationships are preserved. a and chosen from {0.05, 0.1, 0.5) to prioritize node alignment and structural consistency.
Airport Dataset:
Citation Dataset (Citation and ACM Datasets): The Citation dataset often exhibits diverse structural homophily patterns across different distributions, with varying levels of similarity between source and target graphs. These variations necessitate a careful balance between domain alignment and label information from the source graph. The diversity in homophily ratios between the source and target graphs requires moderate a and values balance domain alignment loss (CH) and source classifier loss (Ls). Misalignment in homophily patterns can negatively impact the knowledge transfer process if not adequately addressed. and B are selected from (0.1, ensuring effective trade-off between domain alignment and label supervision.
Social Network Dataset (Blog and Twitch Datasets): Social networks are characterized by a large number of nodes with rich attribute information and high variability in structural patterns. 'hese datasets often feature distinct attribute distributions, making attribute alignment crucial for successful domain adaptation networks typically exhibit higher variance in homophily ratios across source and target domains. This makes alignment particularly sensitive to changes in and B. Lower values are recommended to prevent overfitting to either homophily and heterophilic patterns.a and |3 are chosen from f0.05, 0.1} to foeus attribute alignment while maintaining flexibility for homophily shifts.
The MAG dataset is large and diverse, containing numerous classes with intricate relationships and rich metadata. Both homophily and heterophily aligmment play critical roles in ensuring effective knowledge transfer across domains. Due to its diverse nature, the MAG dataset exhibits a mix of homophily and heterophily patterns. Alignment must consider both structural consistency and attribute- adaptation to account for this diversity. Misalignment in either homophily or heterophily can lead to suboptimal performance. a and B are selected from (0.1, to balance the importance of both homophily and heterophily alignment, ensuring robust performance across diverse classes and relationships.
MAG Dataset:
F. Description of Algorithm HGDA
20

---

Homophily Enhanced Graph Domain Adaptation
0.78
0.66
Accuracy
0.72
048
AccuracyPi
0.54
Accuracy
0.54
0.88
0.40
0.54
05
as
0.48
0.
05
0.36
0.55
0.1
f
0.00
0.0
0.1
(a) C
(b) B E
(c) B1 B2
C
0.72
072
0.78
Aecurasyyan
0.66
0.6
AccurasyM
0.66
0.6
000
06
Accuracy)%)
0.72
0.54
0.42
0.40
0.5
p
0.54
01
05
f
0.4
048
o5
p
0.54
040
0.48
05
Q01
651
(e) CN DE
( CN
FR
gg)
CN JP
CN RU
0.28
Accuray(%))
B54
Accuracy%g)
0.6
0.72
Accurcyy%)
0.44
0.48
ACCUBBOY
048
06
0.42
0.36
005
0.1
0.
042
046
030
0.05
61
as
0336
0.42
0.5
0.1
05
042
03
0.1
0.05
p
61
68
059
(i) DE EN
DE FR
(k) FR
EN
U +
0.66
0.54
Arcuacy/f))
0.54
Accuracy%)
0.88
Accurary(%))
066
Accurcr99
066
0.6
0.48
0.48
0.44
0.42
0.01 f
0.36
0.01
0.5
0.
03
001
f
035
0.05
8.0
87
98
(m) US +
DE
(n)
US +
FR
(0)
US
JP
(p)
US + RU
Figure The influence of hyper-parameters a and 3 on Citation, Airport, ACM and MAG datasets.
21

---

Homophily Enhanced Graph Domain Adaptation
Algorithm 1 The proposed algorithm HGDA
Input: Source node feature matrix x source original graph adjacency matrix A Target node feature matrix X²; Target original graph adjacency matrix A source node label matrix y maximum number of iterations Compute the Å and according to G and G by running.
2 for 1 to do
_ Hr(As, X
7 Hr(18 x
H Hu x))
/ / embedding ng of source graph
Σ HL(A", )")
FF HF[[1 )")
// embedding of target graph
Homophily enhanced domain adaptive between 2ř, and ZF,, Zī: and Z7. and Z and Z / adaptive in three views
Source graph classification 2 and y
10
Domain Adaptive Learning between ~ and ZT
11
12
Calculate the overall loss with (14(
Update all parameters of the framework according the overall loss
Predict the labels of target graph nodes based on the trained framework.
Output: Classification result Y
Types
Datasets
U-B
0.5
U-+E
0.05
0.1
Airport
B-+U
0.1
0.1
E-UU
0.5
0.5
E-BB
0.5
D-A
0.1
0.1
A-C
0.5
Citation
C-AA
0.1
0.1
C-D
0.1
0.1
D-CC
0.1
Blog
B1-+B2
0.1
0.1
B2-+B1
0.1
Twitch
DE-EN
0.1
EN-DD
0.1
DE-FFR
0.5
0.5
FR-EN
0.1
B1-+B2
0.1
0.1
Blog
B2-BB1
0.1
US-CN
US US-DE
0.1
0.1
MAG
US US-
0.1
0.1
US-FFR
0.1
CN-JUS
0.5
0.1
CN-DE
0.1
0.1
CN--JP
CN RU
0.5
0.1
CN-
0.1
Table 5. Experiment hyperparameter setting Value.
22

---

Homophily Enhanced Graph Domain Adaptation
Types
Datasets
#Node
#Edge
#Label
13,599
Airport
Brazil
131
1,038
Europe
5,995
ACMv9
15,556
Citation
Citationvl
8,935
15,098
5
DBLPv?
5.484
8,117
Blugl Blog?
33,471
Blog
2,896
53,836
Germany
9,498
153,138
Twitter
England
7,126
35,324
France
6,549
112,666
ACM3
3,025
2,221,699
ACM
ACM4
57,853
US
132,558
697.450
CN
101.952
285,561
MAG
43,032
126,683
20
JP 37.498
90,944
RU 32,833
67,994
FR 29,262
78,222
Table 6. Dataset Statistics.
23


Reviews:
[{"review_id": "c7EmMKzYY5", "reviewer": "Reviewer_BNmW", "summary": "This paper investigates the graph domain adaptation (GDA) problem highlighting the importance of handling the shift across graph homophily distribution between the source and target graphs. They motivate the issue from both the empirical aspect and from theoretical analysis. Empirically, it has been observed that distinct proportion of different homophily subgroups across the source and target graph will impact the target performance. Theoretically, they show an error bound in terms of homophilic signal shift, heterophilic signal shift, node feature shift and node heterophily distribution shift. To handle the shifts, they propose the algorithm HGDA that align three types of signal shifts using KL divergence together with with source classification loss and target entropy loss. They evaluate the variants of HGDA with DA and GDA baselines on wide range of real world datasets.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your feedback. We would also appreciate your agreement on our method's novelty and effectiveness. Below, we address the concerns and questions raised in the Claims And Evidence, Weaknesses, Theoretical Claims, and Questions For Authors section. Please feel free to reach out if further clarification is required.\n\n# Q1\n\nAs shown in Fig. 5, HGDA achieves balanced performance across different subgroups by processing graph signals with varying levels of homophily through three specialized filters. Specifically, **$HGDA_L$** performs well in homophilic subgroups, **$HGDA_H$** excels in heterophilic subgroups, and **$HGDA_F$** is most effective in subgroups with intermediate homophily levels. The combined contributions of these components lead to an overall balanced performance.\n\n# Q2\n\n1. We acknowledge that continued research into graph-structured data will further enhance the effectiveness of such approaches. However, HGDA method incorporates both homophilic and heterophilic filters that leverage the structural information of the graph.\n  \n2. Our motivation is to address subgroups with varying levels of homophily. To this end, we employ a homophilic filter to extract subgroups with **high homophily**, a full-pass filter for those with **middle homophily**, and a heterophilic filter for subgroups with **low homophily** [1]. This behavior can be observed in Fig. 5. As stated in **Theorem 1**, ${D_{\\text{KL}}(P_S^H | P_T^H)}$ cannot be directly optimized as shown in **Definition1**. However, we can instead minimize the divergence of different homophily-level signals by optimizing ${D_{\\text{KL}}(A^S X^S | A^T X^T)}$, ${D_{\\text{KL}}(X^S | X^T)}$, and ${D_{\\text{KL}}(L^S X^S | L^T X^T)}$, thereby alleviating homophily divergence.\n  \n3. In this paper, we focus on addressing the challenge of homophily shift. We acknowledge that covariate shift, label shift, and particularly conditional structure shift are also critical issues related to homophily in graph domain adaptation (GDA), which we plan to explore in future work.\n  \n\n# Q2\n\nAs noted in **Appendix B**, each experiment was repeated five times, and the reported results represent the average performance. Additionally, we will include the standard deviation of the results in future versions of the paper.\n\n# Q3\n\nThe key difference between **$HGDA_F$** and **DANN** lies in their alignment strategies: $HGDA_F$ employs a KL divergence-based alignment loss, whereas DANN uses an adversarial loss. Moreover, DANN does not incorporate the pseudo-label classification loss on the target graph, which is included in our approach. These differences likely account for the performance gap observed between the two methods. Overall, the performance of different HGDA variants is related to the underlying distribution of the dataset. Specifically, in this [experiment](https://files.catbox.moe/egsaqz.png), **$HGDA_L$** and **$HGDA_F$** tend to perform better on datasets with a higher proportion of homophilic subgroups, while **$HGDA_H$** and **$HGDA_F$** perform better on datasets with a relatively higher degree of heterophily. In the meanwhile, we really appreciate your question, which gives us the opportunity to further improve our manuscript. Specifically, in light of your comments, we will revise **Section 5.3** to further clarify our motivation and avoid potential confusion.\n\n# Q4\n\nWe provide [synthetic experiments](https://files.catbox.moe/9odyw2.png) to validate the effectiveness of our three filter pairs in addressing varying levels of homophily shift. Specifically, we randomly generated five sets of source and target graphs, each containing 300 nodes, where the homophily properties for each subgroup were varied in increments of 0.01. In the picture, the horizontal axis denotes the various homophily subgroups of target graphs, and the vertical axis indicates the performance of different HGDA variants across these homophily levels. The results indicate that $HGDA_L$ performs best in high-homophily scenarios, $HGDA_F$ excels in medium-homophily settings, and $HGDA_H$ is most effective in low-homophily contexts.\n\n# Q5\n\nWe would like to further clarify that, as demonstrated in **Theorem 1**, the performance differences between source and target domain adaptation are influenced not only by component $\\sqrt{D_{\\text{KL}}(P_S^F \\| P_T^F)}$, but also by component **$ L^\\gamma_S(\\phi)$**. Moreover, the effectiveness of **$L^\\gamma_S(\\phi)$** across different adaptation tasks also **depends on the source domain's empirical risk, which indicates an accuracy gap between two adaptation directions**.\n\n# Q6\n\nThe use of KL divergence in our loss function is theoretically motivated. Additionally, incorporating these three loss terms does not significantly increase computational overhead. The overall computational complexity of HGDA remains controlled at **$O(N^2 \\cdot d)$**.", "claims_and_evidence": "**Strength:** \n- Novel shift consideration: focusing on the homophily of subgroups and the entire distribution of node homophily is an interesting and valuable direction in addition to previous GDA works. \n- Empirical justification: The figure 1/7 justify that this type of shift in node homophily exist in the real world datasets. Figure 2/8 try to demonstrate the empirical performance for subgroups with different homophily ratio against distinct homophily divergence.\n\n**Question/Weakness:**\n- It is good that you include Fig 5 as a comparison to Fig 2 after adopting the proposed method. It seems that after HGDA, we have a balance performance with different subgroups instead of related to the level of homophily divergence in fig 2. Can you elaborate more on why your method can handle different divergence level well?", "methods_and_evaluation_criteria": "**Strength:**\n- The method itself is easy to follow and use\n- The method design generally follows the motivation, empirical and theoretical analysis\n\n**Weakness/Questions:**\n- The method primarily focus on feature alignment which might be suboptimal in terms of graph data\n- There is no specific and explicit handle that might target different levels of homophily divergence, i.e. the fourth term in the theoretical analysis. Although it appears to be an intrinsic graph parameter, but it might be able to handle empirically under GNN since it is a main part of your motivation saying this divergence causes performance degradation. \n- Potentially lack control on how to determine the importance of homophilic/heterophilic alignment, should that depend on the distribution of the node homophily? Also, rather complicated loss for training.\n- How this method can handle covariate shift, label shift and conditional structure shift that are previously discussed in GDA literatures? How you position homophily shift with previous discussed shifts and literature.", "theoretical_claims": "The theoretical analysis tends to largely rely on results from previous works with limited contribution in novelty. Also, the analysis regarding KL divergence decomposition of feature distributions tends to be oversimplified and the bound seems to be not tight.", "experimental_designs_or_analyses": "**Strength:**\n- Compared to many baselines and real world datasets\n- Include some visualizations and analysis over parameters and different variants\n\n**Weakness:**\n- No indication of repeated experiments and no standard deviation included in the results\n- Lack analysis in the three variants: For instance, in principle, $HGDA_F$ does not use graph information and should have similar results with DANN, but why it can have better results than graph-based methods and have comparable results with the other two variants?\n- Better if you can provide some synthetic experiments or more detailed analysis over real datasets that detailing how HGDA handle different types/levels of shift", "relation_to_broader_scientific_literature": "This paper helps bring up another issue that exist in GDA", "essential_references_not_discussed": "This paper includes a wide range of relevant literatures but could elaborate more on how their problem and method compared to previous literature.", "other_strengths_and_weaknesses": "Please refer to the above sections", "other_comments_or_suggestions": "some typos: \"Alignemnt\"->\"Alignment\" in subtitle 4.2 and page 6 line 282", "questions_for_authors": "- Question regarding Fig.2: There seems to be a consistent gap between the two accuracy lines indicating two adaptation directions. Your plot shows that the accuracy only relates to the absolute gap in homophily distribution divergence but not with the directions. Can you explain why this is the case? Also, regarding the consistent gap between adaptations from two directions, if it is not attributed to the homophily distribution, what can be the potential cost? e.g. E & B has a large gap in (c) and A3 & A4 has a small gap. \n\n- Question regarding training: How is the loss converge during training since we have a rather complex loss terms with many terms? Why choosing KL divergence in particular to align the distribution of filtered signals.", "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": "CS0OBXz2AD", "reviewer": "Reviewer_4CE1", "summary": "This paper studies the problem of Graph Domain Adaptation problem through analysis homophily shift. This study reveals that homophily distribution shift negatively influences target domain accuracy in an empirical study. Empirical study reveals that homophily discrepancy exists in many benchmarks and provides an essential role in GDA. Through theoretical analysis using the PAC-Bayes framework, the authors prove that the domain shift is bounded by graph homophily distribution shift. Moreover, their theoretical analysis shows that homophily shift can be mitigated through aligning different signals.  The authors conducted comprehensive experiments to validate the algorithm's performance with a sufficient number of baseline methods compared.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your feedback. We would also appreciate your agreement on our method's novelty and effectiveness. Below, we address the concerns and questions raised in the weaknesses section. Please feel free to reach out if further clarification is required.\n\n# Q1\n\n$ KL(Z_L^S \\| Z_L^T) $ aligns the homophilic signal, corresponding to the term $ D_{\\text{KL}}(A^S X^S \\| A^T X^T) $. Similarly, $ KL(Z_H^S \\| Z_H^T) $ directly aligns the graph attributes, corresponding to the term $ D_{\\text{KL}}(X^S \\| X^T) $. Finally, $ KL(Z_F^S \\| Z_F^T) $ aligns the heterophilic signal, which is consistent with the term $ D_{\\text{KL}}(L^S X^S \\| L^T X^T) $ in **Theorem 1**. Specifically, this can be explained as follows. The term ${D_{\\text{KL}}(A^S X^S | A^T X^T)}$ quantifies the divergence in the graph homophily signal, capturing how graph attributes—modulated by the adjacency matrices—differ between the source and target graphs. In contrast, ${D_{\\text{KL}}(X^S | X^T)}$ measures the divergence in the distribution of graph attributes between the two domains. Lastly, ${D_{\\text{KL}}(L^S X^S | L^T X^T)}$ quantifies the divergence in the graph heterophilic signal, where the attributes are modulated by the graph Laplacian matrix.\n\n# Q2\n\nSome early works have addressed graph homogeneity through reconstruction [1] to enhance graph homophily, our work does not directly modify the graph structure due to the computational complexity involved. Instead, **our method focuses on processing homophilic information at varying levels by grouping nodes accordingly**. Inspired by theoretical insights, the model employs low-pass, full-pass, and high-pass filters to capture homophilic signals at different levels. We are pleased to discuss these topics in the related work section of the future version.\n\n[1] Pan E, Kang Z. Beyond homophily: Reconstructing structure for graph-agnostic clustering. International conference on machine learning. , 2023.\n\n# Q3\n\nThanks for your constructive comment! Following your suggestion, we also conducted [additional experiments](https://files.catbox.moe/ewkc85.png), evaluating HGDA performance on ogbn-arxiv dataset. Specifically, we report the performance of HGDA on three tasks. As for ogbn-arxiv networks, we choose years to separate networks, which are collected from **1950- 2016 (50- 16), 2016- 2018 (16- 18), and 2018- 2020 (18- 20)**. Our results demonstrate that while their method performs well, our approach exhibits **outperformance**, highlighting the importance of minimizing homophily shift. We will include these baseline methods and additional evaluation metrics in future versions.\n\nThank you for your comment regarding typo problems. We apologize for this and have carefully reviewed and corrected them throughout the paper in the future version.", "claims_and_evidence": "Yes. The claims made in the submission are generaly supported by both theoretical and experimental evidence.", "methods_and_evaluation_criteria": "Yes. The proposed method make sense in reducing graph homophily discrepancy and the experimental evaluation appears reasonable and is conducted using widely accepted criteria.", "theoretical_claims": "Yes. I have reviewed the proofs of the theoretical claims in the paper in the supplemental material particular for Theorem 1.", "experimental_designs_or_analyses": "The exoerimental designs are generally sound whicn include the ablation study and parameter analysis.", "relation_to_broader_scientific_literature": "The key contributions of the paper are related to the filed of graph domain adaptation and the homophily shift is of particular studied.", "essential_references_not_discussed": "Some recent advancements in GDA might also need to cite, such as those discussed in [1].\n\n[1] Zhang, Zhen, et al. \"Aggregate to Adapt: Node-Centric Aggregation for Multi-Source-Free Graph Domain Adaptation.'' *The Web Conference*, 2025", "other_strengths_and_weaknesses": "Strengths:\n\n- This paper highlights the importance of homophily distribution discrepancy in GDA and empirically investigates its impact on GDA performance.\n\n- This paper is technically sound and novel. In theoretical analysis part, it demonstrates that the heterophily distribution shift between the source and target graphs can mitigate through homophilc signal, graph attribute signal, and heterophilic signal.\n\n- HGDA method is theoretically motivated and aligns the three graph signals using KL divergence, ensuring consistency with the theoretical findings.\n\n- The experiments are convincing and the experiment details are complete with detailed experiment description in the supplemental material.\n\nWeaknesses:\n\n- The explanation of the relationship between the proposed method and Theorem 1 in Section 4.2 could be clarified, particularly regarding their differing motivations.\n\n- The paper should expand the discussion in the related work section to include connections to other studies that address structural shift in GDA. Since homophily is fundamentally a structural property, drawing parallels with existing approaches to structural shift could provide a broader contextual foundation for the study.\n\n- Although the paper has generally sufficient experimental data set, it could benefit from additional experiments on other benchmarks for GDA’s target node classification task, e.g., ogbn-arxiv.", "other_comments_or_suggestions": "Typos:\n- Line 282 \"Alignemnt\"\n\n- Line 98 \"homophilc\"", "questions_for_authors": "See the weakness above.", "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": "TJlwPrKAOi", "reviewer": "Reviewer_6Xce", "summary": "This paper proposes a novel Graph Domain Adaptation algorithm which solves graph homophily disparity for effective domain alignment. It shows that homophily distribution shifts exist wildly in GDA datasets and could damage GDA performance in both empirically and theoretically ways. Inspired by theoretical results, it also provides a method to mitigate this discrepancy through cross-channel homophily alignment (HGDA).", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your constructive feedback! Below, we address the concerns and questions raised in the weaknesses section. Please feel free to reach out if further clarification is required.\n\n# Q1\n\nThanks for your constructive comment! Following your suggestion, we also conducted [additional experiments](https://files.catbox.moe/ewkc85.png), evaluating HGDA performance on **ogbn-arxiv** dataset. Specifically, we report the performance of HGDA on three tasks. As for ogbn-arxivl networks, we choose the year to separate networks, which are collected from **1950-2016(50-16), 2016-2018(16-18), and 2018-2020(18-20)**. As for Twitch **RU and ES**, we are pleased to provide their experiment, which is as [follows link](https://files.catbox.moe/9hxty1.png). Our results demonstrate that while their method performs well, our approach exhibits **outperformance**, highlighting the importance of minimizing homophily shift. In future versions, we will include these baseline methods along with additional evaluation metrics.\n\n# Q2\n\nWe apologize for any misunderstanding caused by the previous lack of clarity. To clarify, overall graph node homophily ratio is $\\; \\int_{0}^{1} v \\,\\cdot\\, H^v_{\\text{node}} \\,\\mathrm{d}v.$\n\nwhich actually is our **Definition 1 (Graph-Level Node Heterophily Distribution)** in **Section3.3**. This method computes the homophily distribution across the entire graph. As shown in **Fig. 1**, in the Airport dataset, while the overall graph-level node heterophily distributions of the BRAZIL and EUROPE subgraphs are relatively similar, significant differences exist in the local homophily subgroups. These observations highlight the need for our model to handle homophily shifts effectively at different levels.\n\n# Q3\n\nTo address your concern, we provide [experimental results](https://files.catbox.moe/egsaqz.png) that report the classification accuracy on target graph subgroups with varying levels of homophily. We also provide [synthetic experiments](https://files.catbox.moe/9odyw2.png) to validate the effectiveness of our three filter pairs in addressing varying levels of homophily shift, which detail can be found in **Reviewer BNmW** in **Q4**. The results show that **$HGDA_L$** performs best in subgroups with high homophily, **$HGDA_F$** performs best in subgroups with intermediate homophily, and **$HGDA_H$** performs best in subgroups with low homophily. These findings support the effectiveness of our method in aligning graph signals across different levels of homophily. Therefore, we can conclude that these three modules provide different roles in HGDA.\n\n# Q4\n\nRegarding **Definition 1 (Graph-Level Node Heterophily Distribution)**, $P_G^H$ captures structural information inherent to the graph, as observed in nature [1, 2]. Consequently, unless the graph topology itself is directly altered, $P_G^H$​ remains a fixed quantity. As a result, ${D_{\\text{KL}}(P_S^H \\| P_T^H)}$ is also an intrinsic and fixed value. Following your suggestion, we will address these concerns and provide clarification in a future version of the paper.\n\n[1] Pan E, Kang Z. Beyond homophily: Reconstructing structure for graph-agnostic clustering. International conference on machine learning. , 2023.\n\n[2] Xie X, Chen W, Kang Z. Robust graph structure learning under heterophily. Neural Networks, 2025.\n\nThank you for your comment regarding Table line problems. We apologize for this and have carefully reviewed and corrected them throughout the paper in the future version.", "claims_and_evidence": "The paper claims that homophilic ratio divergence exhibits a negative correlation with the classification accuracy of target graph nodes. It provides empirical results in Figure 2, which contain target node classicifaction accuracy percent difference and homophily distribution shift in each corresponding subgroups.", "methods_and_evaluation_criteria": "While most aspects of the evaluation are comprehensive, with performance reported over eight recent baselines on six datasets, the evaluation benchmark is partially limited. For benchmark Twitch [1], Russia (RU) and Spain (ES) are not involved. I also want to see the HGDA performance in ogbn-arxiv[2], which involves temporal discrepancy with different publication years.\n\n[1] Liu M, Fang Z, Zhang Z, et al. Rethinking propagation for unsupervised graph domain adaptation[C]. AAAI 2024\n\n[2] Liu M, Zhang Z, Tang J, et al. Revisiting, Benchmarking and Understanding Unsupervised Graph Domain Adaptation[J]. NeurIPS 2024", "theoretical_claims": "This paper theoretically justifies the impact of a homophily distribution shift on GDA and demonstrates that this discrepancy can be mitigated by addressing the homophilic and heterophilic signals.", "experimental_designs_or_analyses": "I check the validity of experiments, consisting of performance comparison, ablation study, and hyper-parameter and model efficient experiment analysis.", "relation_to_broader_scientific_literature": "This paper provides a novel view on GDA tasks. Its method has theoretical guarantees. Although SA-GDA[1] is partially similar to HGDA in utilizing graph signal in spectral space, I recommend that the authors discuss their differences with that paper in related work.", "essential_references_not_discussed": "To my knowledge, the paper discusses the most essential references.", "other_strengths_and_weaknesses": "Strengths:\n\n1.This paper presents a well-founded study supported by both theoretical analysis and experimental evidence. \n\n2.The method proposed in this paper is grounded in meaningful theoretical research.\n\nWeaknesses:\n\n1.The experimental evaluation in this paper is somewhat limited. As noted in the Evaluation Criteria, a more comprehensive experiment across additional datasets would strengthen the study and improve its validity. \n\n2.The dotted line in the two sub-graphs of Figure 1 represents the overall graph node homophily ratio. However, the paper does not clearly explain the method used to calculate this value.  \n\n3.Can the authors clarify the impact of the three proposed alignment modules, namely ${\\text{KL}}(Z_L^S \\| Z_L^T)$, ${\\text{KL}}(Z_H^S \\| Z_H^T)$, and ${\\text{KL}}(Z_F^S \\| Z_F^T)$, on the classification performance of nodes with different homophily ratios? Intuitively, these modules should play distinct roles in the alignment process. \n\n4.Why is ${D_{\\text{KL}}(P_S^H \\| P_T^H)} $, one of the terms in Theorem 1, considered a fixed value? Additionally, why is it not subject to optimization?", "other_comments_or_suggestions": "In Table 1, a vertical line between the Airport and ACM datasets appears to be missing.", "questions_for_authors": "Additional experiments, particularly on the ogbn-arxiv dataset, would help validate HGDA's performance in addressing temporal discrepancies. Furthermore, a running time analysis and comparisons with a broader set of baseline models are needed to strengthen the evaluation. Other questions refer to other strengths and weaknesses.", "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": "XOndXsY4Fo", "reviewer": "Reviewer_oEYM", "summary": "This paper investigates graph domain adaptation through homophily alignment. The authors argued that the graph homophily has been overlooked by existing graph domain adaptation works. To address this issue, the authors first conduct some empirical analyses and find that the homophily discrepancies indeed exist in the widely used benchmarks. Then, the authors proposed a model to use mixed filters to smooth graph signals and align homophily discrepancies between source and target graphs. Experimental results on 5 public datasets show that it can achieve satisfied performance compared with recent baselines.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your appreciated feedback. Below, we address the concerns and questions raised in the weaknesses section. Please feel free to reach out if further clarification is required.\n\n# Q1\n\n**Justification:** Our model is designed to separately process graph signals with different levels of homophily. Specifically, we use $AX$ to extract homophilic signals, $IX$ to obtain full-pass signals, and $LX$ to capture heterophilic signals. Furthermore, this design aligns with our theoretical analysis, which shows that the entire model can be optimized by minimizing the distributional shifts of ${D_{\\text{KL}}(A^S X^S | A^T X^T)}$, ${D_{\\text{KL}}(X^S | X^T)}$, and ${D_{\\text{KL}}(L^S X^S | L^T X^T)}$.\n\n**Laplacian matrix $L$:** Regarding $L$, There might be some misunderstanding. In fact, the graph **Laplacian matrix can be viewed as a high-pass filter that obtains heterophilic signals**—a perspective that has been adopted in several existing works [1, 2, 3] (e.g., in Section2.1 of [1], it says \"To address the heterophily challenge, high-pass(HP) filter $L$ is often used to replace low-pass(LP) filter $A$\"). To the best of our knowledge, we are unaware of any graph theory that contradicts utilizing a Laplacian matrix to obtain heterophilic signals. We are pleased to provide more clarification and havea more detailed discussion with you regarding this matter if you still have concerns.\n\n[1] Luan S, Hua C, Xu M, et al. When do graph neural networks help with node classification? Investigating the homophily principle on node distinguishability. Advances in Neural Information Processing Systems, 2023.\n\n[2] Luan S, Hua C, Lu Q, et al. Revisiting heterophily for graph neural networks. Advances in neural information processing systems, 2022.\n\n[3] Li B, Pan E, Kang Z. Pc-conv: Unifying homophily and heterophily with two-fold filtering. Proceedings of the AAAI conference on artificial intelligence. 2024.\n\n# Q2\n\nThanks for your constructive comment! Following your suggestion, we also conducted additional experiments, evaluating **MAG** using macro-F1 and **Twitch** using AUC to address your concern. Due to word limitations, we have provided visualizations of these tables in the supplementary material, accessible via the following link [MAG](https://files.catbox.moe/e1ppdo.png) and [Twitch](https://files.catbox.moe/rw69ik.png).\n\n# Q3\n\nWe acknowledge the importance of comparing our approach with recent advancements, including TDSS, A2GNN, GraphAlign [1*,2*,3*]. We report the performance of HGDA and the baseline methods on the [Airport, ACM, Blog](https://files.catbox.moe/hnbk9e.png) and [Citation](https://files.catbox.moe/or0weu.png) datasets. For the results on **MAG** and **Twitch**, please refer to our response to **Q2**. Our results demonstrate that while their method performs well, our approach exhibits **outperformance**, highlighting the importance of minimizing homophily shift. In future version, we will include these baseline methods along with additional evaluation metrics.\n\n# Q4\n\nThank you for your valuable comment. We believe there might be a slight misunderstanding regarding the notion of \"enhancing graph homophily\" in the context of our work. Our paper does not aim to improve or increase the inherent homophily of the graph itself. Instead, our focus is on highlighting the homophily shift that occurs between the source and target domains in graph domain adaptation (GDA), and proposing a method to mitigate this shift. We will further revise our paper to clarify this point. Regarding the justification on this point, we provide [experimental results](https://files.catbox.moe/egsaqz.png) that report the classification accuracy on target graph subgroups with varying levels of homophily. The results show that **$HGDA_L$** performs best in subgroups with high homophily, **$HGDA_F$** performs best in subgroups with intermediate homophily, and **$HGDA_H$** performs best in subgroups with low homophily. These findings underscore the effectiveness of our method, which employs a combination of filters to mitigate homophily discrepancies at various levels.\n\n# Q5\n\nRegarding the concern about **$Z_L$**, **$Z_F$**, and **$Z_H$**, we would like to clarify that these embeddings are obtained by applying homophilic, full-pass, and heterophilic filters, respectively. In **Table 1**, **Table 2**, and **Table 3**, the variants **$HGDA_L$**, **$HGDA_F$**, and **$HGDA_H$** exclusively utilize **$Z_L$**, **$Z_F$**, and **$Z_H$**, respectively. The results of the main experiments show that each variant performs differently across datasets, which we attribute to the intrinsic homophily distribution characteristics of each dataset. The effects of **$Z_L$**, **$Z_F$**, and **$Z_H$** are further demonstrated by the experiments discussed in **Q4**.\n\nFor clarification, the GCN baseline under the standard unsupervised GDA setting employs a two-layer GCN architecture combined with an MMD loss for domain alignment.", "claims_and_evidence": "The key claim is not convincing:\n\nThe authors propose to utilize three filters to learn graph signals, which is defined as homophilic filter, full-pass filter and heterophilic filter. Based on the Equations (8), (9) and (10), the authors use $AX$, $IX$ and $LX$ to represent the homophilic, full and heterophilic signals in graph. Why Laplacian matrix $L$ can represent the heterophilic signals, which is contradictive to the graph spectral theory.", "methods_and_evaluation_criteria": "The evaluation metric is not accurate. As different datasets have different properties, the accuracy (ACC) metric cannot reflect the model’s true performance on these datasets. For instance, MAG dataset’s labels are highly skewed, and macro-F1 score should be used as the evaluation metric. Twitch dataset contains two labels and should use AUC as the evaluation metric.\n\nThe model’s design also lacks justification and is contradictive to the graph spectral theory.", "theoretical_claims": "I did not carefully check the full proofs in the Appendix due to limited time.", "experimental_designs_or_analyses": "Although the authors use 5 different datasets in the experiments, the authors use accuracy for all the datasets, which is not reasonable.\n\nAs for the findings, in Figure 2, the authors get the results by using GCN with standard unsupervised GDA setting as evaluation model. However, it is unclear what is the standard unsupervised GDA setting, i.e., MMD or adversarial training.", "relation_to_broader_scientific_literature": "The key ideas of combining different types of graph signals are not new, which is like multi-view or multi-channel graph convolutional network.\n\nWang X, Zhu M, Bo D, et al. Am-gcn: Adaptive multi-channel graph convolutional networks[C]//Proceedings of the 26th ACM SIGKDD International conference on knowledge discovery & data mining. 2020: 1243-1253.", "essential_references_not_discussed": "The authors fail to compare and discuss the following highly relevant papers: \n\n[1] Huang R, Xu J, Jiang X, et al. Can Modifying Data Address Graph Domain Adaptation?[C]//Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 2024: 1131-1142.\n\n[2] Chen W, Ye G, Wang Y, et al. Smoothness Really Matters: A Simple yet Effective Approach for Unsupervised Graph Domain Adaptation[J]. arXiv preprint arXiv:2412.11654, 2024.", "other_strengths_and_weaknesses": "Pros:\n\n1.\tGraph domain adaptation could be a promising application, which helps alleviate distribution shift problem.\n\n2.\tExperiments are conducted on 5 public datasets including both small- and large-scale datasets.\n\n3.\tAblation studies and theoretical analyses are given to show the effectiveness of the proposed model.\n\nCons:\n\n1.\tThe design of the model needs more justification. The authors propose to utilize three filters to learn graph signals, which is defined as homophilic filter, full-pass filter and heterophilic filter. Based on the Equations (8), (9) and (10), the authors use $AX$, $IX$ and $LX$ to represent the homophilic, full and heterophilic signals in graph. Why Laplacian matrix $L$ can represent the heterophilic signals, which is contradictive to the graph spectral theory.\n\n2.\tThe evaluation metric is not accurate. As different datasets have different properties, the accuracy (ACC) metric cannot reflect the model’s true performance on these datasets. For instance, MAG dataset’s labels are highly skewed, and macro-F1 score should be used as the evaluation metric. Twitch dataset contains two labels and should use AUC as the evaluation metric.\n\n3.\tThe key baselines are missing. More recent baselines should be discussed and compared. Please refer to the reference below [1,2,3].\n\n4.\tIt is not clear how the proposed model enhances the graph homophily. More justification should be given.\n\n5.\tMore ablation studies should be given to show the necessary to adding the representations of $Z_L$, $Z_H$ and $Z_F$.\n\nReference:\n\n[1] Huang R, Xu J, Jiang X, et al. Can Modifying Data Address Graph Domain Adaptation?[C]//Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 2024: 1131-1142.\n\n[2] Liu M, Fang Z, Zhang Z, et al. Rethinking propagation for unsupervised graph domain adaptation[C]//Proceedings of the AAAI Conference on Artificial Intelligence. 2024, 38(12): 13963-13971.\n\n[3] Chen W, Ye G, Wang Y, et al. Smoothness Really Matters: A Simple yet Effective Approach for Unsupervised Graph Domain Adaptation[J]. arXiv preprint arXiv:2412.11654, 2024.", "other_comments_or_suggestions": "There are too many typos in the paper:\n\n1.\tLines 29 to 31, as shown in Figure 1(a), “…ACM3 and ACM4…”. It should be Figure 1(b).\n\n2.\tLines 143 to 144, there are two “where”.\n\n3.\tLines 190 to 191, “heterophilc” should be heterophilic.\n\n4.\tLin3 239, 257, 271, I don’t understand what $H_LH^{l-1}W_L^{l-1}$, $H_FH^{l-1}W_F^{l-1}$ and $H_HH^{l-1}W_H^{l-1}$ mean.\n\n5.\tIn Appendix table 6, the dataset should be Twitch not Twitter.", "questions_for_authors": "Please refer to the weakness part.", "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:

Meta-review: This paper tracks an important problem: graph domain adaptation. Given the graph data is more and more important in real applications, investigating the effect brought by distribution shifts is important. The main contribution of this paper is to find that homophily discrepancies exist in benchmarks and degrade GDA performance from both empirical and theoretical aspects. This is a new contribution to this field.

The reviewers had concerns regarding the technical novelty used in this paper. Indeed, the final methodology is not entirely new, as some high-level ideas already exist in the literature. However, given the contribution of this paper lies in the findings above, this paper still has enough contributions to the field. This is also agreed by reviewers who are all positive towards this paper at the end of the discussion.
Decision: Accept (poster)