FDGen: A Fairness-Aware Graph Generation Model
Authors: Zichong Wang
Wenbin Zhang
Venue: ICML 2025 poster (2025)
Keywords: Fairness
Graph Learning
Graph Generation
Primary area: social_aspects->fairness

Abstract: Graph generation models have shown significant potential across various domains. However, despite their success, these models often inherit societal biases, limiting their adoption in real-world applications. Existing research on fairness in graph generation primarily addresses structural bias, overlooking the critical issue of feature bias. To address this gap, we propose FDGen, a novel approach that defines and mitigates both feature and structural biases in graph generation models. Furthermore, we provide a theoretical analysis of how bias sources in graph data contribute to disparities in graph generation tasks. Experimental results on four real-world datasets demonstrate that FDGen outperforms state-of-the-art methods, achieving notable improvements in fairness while maintaining competitive generation performance.

FDGen: A Fairness-Aware Graph Generation Model
Zichong Wang'
Wenbin Zhang
Abstract
Despite showing promising results, most graph generation models suffer from fairesss issues (Wang et al., 2023c), rais- ing ethical and societal concerns, particularly in high-stake decision Decision-making scenarios such as healthcare (Yu et al., 2020), credit scoring (Shumovskaia et al., 2020), and crime prediction (Wang et al., 2025b). Consider a credit scoring scenario where financial institutions need synthetic data for partner collaboration. While graph generation models can protect individual privacy by creating synthetic graphs from real data, they may amplify existing biases (Wang & Zhang, 2024). For example, if the original data shows ethnic clustering in financial relationships, the generated graphs often strengthen these patterns, creating denser con- nections between people of the same ethnicity. These am- plified structural biases then affect downstream financial decisions (Wang et al., 2025a).
Graph generation models have shown significant potential across various domains. However, de- spite their success, these models often inherit so- cietal biases, limiting their adoption in real-world applications. Existing research on fairness in graph generation primarily addresses structural bias, overlooking the critical issue of feature bias. To address this gap, propose FDGen, a novel approach that defines and mitigates both feature and structural biases in graph generation models. Furthermore, we provide a theoretical analysis of how bias sources in graph data contribute to dis- parities in graph generation tasks. Experimental results on four real-world datasets demonstrate that FDGen outperforms wate-of-theear methods, achieving notable improvements in fairness while maintaining competitive generation performance.
To this end, preliminary efforts have been made to explore fairness within graph generation models. For instance, Fair- Wire (Kose & Shen, 2024b) designs a fairness regularizer and leverages the proposed fair regularizer in a generative model to mitigate graph structure bias. However, FairWire, like existing fair graph generation models (Zheng al., 2024), focuses solely on addressing structural bias, where nodes connect predominantly with neighboring nodes shar- ing the same sensitive attributes. For example, in the gener- ated graph shown in Figure I (b), the central male node vl, compared with the original graph in Figure (()), maintains connections with male nodes 02 and U3, adds new connec- tion with male node U4, and loses its original connections with female nodes Us and ug, leading to significantly higher recommendation rates within sensitive groups, potentially causing social segregation (Hofstra et al., 2017). However, all existing methods overlook feature bias, which arises when the generated non-sensitive attributes exhibit distri- butional disparities across subgroups. Still in Figure 1, the original graph in Figure (a) depicts equal incomes across gender groups, whereas the generated graph in Figure (b) shows male nodes with higher incomes than female nodes ($370,000 vs. $250,000), leading to biased downstream applications where models trained on this synthetic data learn to expect higher incomes from male applicants. In addition, feature bias is closely intertwined with structural bias, as node features propagate through the network struc- ture. Therefore, it cannot be overlooked when aiming for
1. Introduction
Graphs naturally appear in many real-world scenarios, from social network analysis (Grover et al., 2019), fi- nancial markets (Wang et al., 2023a), and recommen- dation systems (Wang et al., 2019) to the Internet of Things (Kong et al., 2023). In this context, deep learn- ing on graph-structured data has attracted increasing at- tention and inspired many graph learning frameworks in recent years (Kang al., 2022; Wang et al., 2024c; 2025h). Among them, graph generation models have become cru- cial components of the graph machine learning framework, serving purposes such as data augmentation (Chakrabarti & Faloutsos, 2006), anomaly detection (Akoglu et al., 2008), and enabling
data sharing (Kose & Shen, 2024b). Thus, creating synthetic graphs with graph gen- erative models becomes instrumental in applications over interconnected systems.
'nnghtt Foundation School of Computing and Information Sciences, Florida International University, Miami, USA. Corre- spondence to: Wenbin Zhang <wenbin.zhang @ fiu.edu>.
Proceedings of the ndnd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

---

FDGen: A Fairness-Aware Graph Generation Model
truly fair graph structure generation.
smoothness. Based on this, we design new diffusion-based fair graph generation framework that leverages the proposed regularizer to achieve fair graph generation.
It is therefore of social importance to account for multiple biases to generate fair graphs, as shown in Figure 1 (c). Specifically, U1 maintains balanced connections with both male (V2, vt) and female neighbors (r', va), demonstrat- ing equal connectivity across gender groups. Additionally, while preserving inherent group-specific characteristics, the node attributes, such as income, show similar distributions across different groups, eliminating feature bias. To achieve such fair graph generation, several challenges need to be ad- dressed: i) Difficulty in measuring feature bias: Existing fair graph generation models primarily address structural bias by using statistical comparisons of inter- inter-group group con- nectivity. However, measuring node feature bias presents a critical challenge, as real-world graphs contain diverse types of node features (e.g., categorical zip codes, continuous in- come values) with different scales and distributions that can- not be directly compared using simple statistical measures. ii) Difficulty in mitigating multiple types of bias during generation: Unlike independent and identically distributed (II) data, graph generation requires ensuring fairness in both node features and graph structure. Furthermore, node features influence the formation of graph structure, and the graph structure affects the generation of node features. This interdependence makes it challenging to design universal fairness constraints that can effectively reduce both types of bias simultancously. iii) Difficulty in distinguishing group identity information: While we aim to mitigate unfair dif- ferences between groups, we need to preserve legitimate group-specific characteristics. For instance, while we seek equal treatment in non-sensitive attributes like income or credit scores, we should maintain natural group differences in physical characteristics (e.g., facial hair in males). The key challenge is to distinguish between biases that require mitigation and inherent group characteristics that should be maintained, thereby ensuring generated graphs that are both fair and realistic.
Our main contributions can be summarized as follows: i) Problem. We formalize the fair graph generation problem and identify unique challenges motivated by real applica- tions. ii) Framework. We proposed a novel fairness- aware graph generation model to mitigate structural bias and fea- ture bias during the graph generation while guaranteeing graph quality and enhancing fairness. iii) Experimental Evaluation. We conduct extensive experiments on four real- world datasets, demonstrating the superior performance of the proposed method over other state-of-the-ar fairness methods.
2. Related Work
Synthetic Graph Generation. Generating synthetic graphs has been a longstanding research topic (Bojchevski et al., 2018: Kong et al., 2023), with deep generative models proving particularly successful (Li et al., 2019). Exist- ing approaches include one-shot methods, often based VAEs (Simonovsky & Komodakis, 2018; Liu et al., 2018) or GANs (De Cao & Kipf, 2018; Bojchevski et al., 2018), which generate all edges simultaneously from la- tent embeddings but may degrade structural fidelity due to independence assumptions. In contrast, autoregressive models generate graphs by sequentially adding nodes and edges. These approaches, implemented through recurrent networks (Dai et al., 2020) or reinforcement learning (You et al., 2018), capture complex structural patterns and allow constraints during generation, but remain sensitive to node ordering (Huang et al., 2022). More recently, diffusion- based methods have emerged (Liu et al., 2019; Niu et al., 2020; Chen et al., 2023; Li et al., 2023), defining a Markov chain of diffusion steps that gradually add noise to data, then learn to reverse the inference path to generate data from noise remains unexplored in synthetic graph generation, limiting these models' use in high-stakes scenarios. This has created a need to develop fairer graph generation methods.
et al., 2015). However, faimess
To tackle the aforementioned challenges, we propose novel framework, FDGen (short for Fair Diffusion for Graph Generation) to ensure the fairness of the graph generation model. To the best of our knowledge, this is the first work to simultaneously miligute multisource biases arising from sensitive attributes in graph generation models. Specifi- cally, we first carry out a theoretical analysis investigating the sources of bias in the graph generation model. Guided by the theoretical findings, we proposed a novel fairness regularizer, which can be interpreted as encouraging each node to weightily aggregate representations of other nodes with different sensitive attributes of the central node and weightily subtract representations of other nodes with the same sensitive attribute, which can alleviate over- associa- tion of the learned representation with sensitive attributes, resulting in fair representations with good utility ensured by
Fairness-aware Graph Generation Model. Fairness is a widely-existing issue of graph learning systems and has received increasing research attention in recent years (Wang et al., 2025d;c; 2024a; Wang & Zhang, 2024; Zhang et al., 2024; Zhu et al., 2024). Despite these advances, most ex- isting methods focus on classification tasks, leaving the do- main of graph generation models largely unexplored (Zhang ct al., 2025). To this end, a small number of works (Rah- man et al., 2019; Wang et al., 2023c; Zheng et al., 2024) have started to investigate fairness in graph generation mod- els, which can be divided into two categories: i) Fair link prediction and ii) Fair graph structural generation. Specif-
2

---

FDGen: A Fairness- Graph Generation Model
%
Gante=1
Gasier 0
V7
leight Mosache Edacation Gradlatt 3700000
Height 53
Mustacte 0
Education Graduase lacosse 250,000
Synthetic
Synthetie
V
(b) Others
Real
Mastade-
Ixhemnse Uindua
Ihcoes 280/00
59
VA
V/2
Heght Iidasance (rnuaae Incomz 225,000
Muskadi- -
Height 91
Garder -
V/
V7
Eduastio Gialuato Inceree 255.003
Masbote-0
Synthetic
Syathetic
Educatos Grolutto
Incees-- 290100
Real
(a) Original
V2
Ours
Figure toy example of biases in graph generation is shown, where black lines represent original edges, gray dashed lines indicate removed inter-group edges, and orange lines denote newly added intra- intra-group group edges.
ically, fair link prediction focuses on achieving unbiased predictions of dyadic relationships among graph nodes. For instance, FAIRLP (Li et al., 2022) was designed to modify the training graph to balance the distribution of intra-group and inter-group links while preserving the network char- acteristics of the graph. This enhancement improves the representation of underrepresented groups achieve fair link prediction. Unlike fair link prediction, fair graph struc- tural generation measures graph structural bias at the graph level and aims to reduce the distribution difference between the generated graph and the original graph's inter- and intra- group edges. For instance, FairGen (Zheng et al., 2024) achieves fair graph structural generation by incorporating parity constraints to minimize the difference in reconstruc- tion loss between the generated graph and the original graph across different subgroups. However, these methods, focus solely on ensuring fairness in graph structure generation, neglecting potential biases in node information generation, which are crucial for achieving truly fair graph generation.
cates that there exists edge 6 between node v and vy. and A., 0 otherwise. In this paper, assume that both ground-truth labels and sensitive attributes are binary vari- ables for convenience. We let S E 1)x1 to denote the binary sensitive attributes, where is the sensitive attribute of e We use S. = AA 0 E V = 0} denotes the deprived group (e.g., female) and S (V e2 E Vl8 = 1} denotes the favored group (e.g., male). For node classification, each node is also associated with one-hot ground-truth node label y, where is the label of v We also assume y: = 1 denotes the granted label and label. In addition, we let G., represent the ego graph of center node v, which includes important neighbor nodes of the central node.
0 denotes the rejected
4. The Proposed Framework: FDGen
This section introduces FDGen, framework built upon the graph diffusion model (Kong et al., 2023) to mitigate both structural and feature bias for fair graph generation. Given the correlation between these biases, FDGen developed to adaptively mitigate them during generation, leveraging the flexibility and tractable probability distributions of diffusion models. Specifically, bias types in graph generation first defined, along with theoretical foundations for fairness regularizers (Section 4.1). Next, we describe how FDGen isolates sensitive information into independent components to measure generation discrepancies and apply fairness con- straints (Section 4.2). Finally, the FDGen model and its training objectives are presented (Section 4.3).
In contrast to existing work, this paper proposes a fair graph generation model that addresses both graph structural bias and feature bias, with its design informed by theoretical analysis. In addition, the bias mitigation approach is flexible, allowing it to be applied in both link prediction models and generative models.
3. Notation
In this paper, we formalize the graph generation problem in the context of an undirected graph G = EV, it would contain | nodes and | edges. The feature matrix for the graph is denoted as X R where i-th row rep- resents a d-dimensional feature vector of the i-th node e;- A E {0, 1) jaxa is the adjacency matrix where Aij = 1 indi-
4.1. Fair Graph Generation Regularizer
We first examine the root causes of biases in graph gener- ation, laying the groundwork for fairness regularization
3

---

FDGen: A Fairness-Aware Graph Generation Model
strategy to mitigate them. Specifically, graph generation models are vulnerable to bias through two main mecha- nisms: i) nodes with the same sensitive attributes tend to form denser connections, creating structural bias, and ii) the node feature distributions often show systematic differences across demographic groups, leading to feature bias. In addi- tion, these biases can be mutually reinforcing, as nodes with similar features are more likely to connect, and connected nodes influence each other's feature representations. Spe- cific to graph diffusion models, these biases can be further amplified during generation. Specifically, a diffusion- graph generation model defines a forward Markov transition kernel (xx xt-1) to gradually corrupt the training data into a simple noise distribution. The model then learns a reverse denoising transition po ( xx) using a neural network. During this reverse process, GNN-style message passing aggregates information from neighboring nodes to preserve both topological structure and node features. However, this message-passingg mechanism can exacerbate existing biases through two effects: First, by smoothing rep- resentations of connected nodes, it strengthens segregation between different sensitive groups, amplifying graph struc- tural bias. Second, it reinforces the association between node representations and sensitive attributes, exacerbating feature bias in the generated graphs.
R6 hgp
Σ
(1gg)) bgy")
+
Σ Vs, vinyele,
s(Dgl" mnp")
sunyy Ka
2
K( (nz!.) b2!"))
Vaal-
[Vs)
where k(.,-) is a kernel function (e.g., RBF kernel). A large hgD (1) indicates substantial divergence between Vs, and Vs, the non-sensitive channel (i.e., sub node representation). Conversely, small MMD implies a better alignment of non-sensitive embeddings, reducing unfair discrimination risk in downstream tasks. In addition, this measure can be simplified to a direct Euclidean distance between mean embeddings, and extends naturally to multiple sensitive attributes.
Building on this representation separation measurement, FDGen proceeds in three steps. First, we analyze how representation discrepancy emerges during GNN-based ag- gregation, establishing an upper bound to understand its propagation through network layers (Theorem 4.2). Sec- ond, we demonstrate how this representation discrepancy directly influences group disparity, showing that reducing representation differences leads to improved demographic parity (Theorem 4.3). Finally, guided by these theoretical insights, we propose a fairness regularizer that simultane- ously addresses both structural and feature bias by aligning non-sensitive representations while maintaining appropriate group-specific differences.
To this end, a theoretically grounded fairness regularizer is proposed to mitigate both structural and feature bias simultaneously. Starting with node representation differ- ences (h'p). the commonly used approach is to measure them between groups as hi, = h's, h's, (h's, and h's, denote the node representations for deprived and favored groups, respectively). However, while this captures over- all representation differences between subgroups, it fails to account for the distinct roles of sensitive information, as nodes with different sensitive attributes should have differ- ent sensitive-related components while maintaining similar censitive-irrellvann components. To this end, we separate node representations into sensitive-related representations f.S and sensitive-irreleean representations h This sep- aration allows us to minimize the differences in sensitive- irrelevant components (h.-S) while maintaining appropriate differences in sensitive-related components (h (.S, ), thereby preserving group identity while mitigating bias, as detailed in Definition 4.1.
We begin with the first step of analyzing representation discrepancy. During GNN message-passingg node repre- sentations are influenced by both their neighbors and the network structure. Theorem 4.2 quantifies this influence by providing an upper bound on the representation discrepancy between sensitive groups, revealing how bias can accumu- late across layers (proof in Appendix).
(1) between the represen- Theorem 4.2. The discrepancy hgD lations of nodes in sensitive group Sa and the rest of the nodes at the h GNN layer can be upper bounded by:
hgD
(1) I 3
(Vsg + [Vs Voy1) |1100 - 1191
Σ
1-1 h5, ;1))))1))
JES,
+ |
Definition 4.1 (Sensitive-irrelaeed Representation Discrep- ancy). Let Vs, and Vs, be two subgroups corresponding to distinct values Sa. Sy e S of sensitive attribute, with Sa # Sy. Suppose each node e; has a non-sensitive repre- sentation h at layer I, intended to be independent of the sensitive attribute S. We quantify any unintended discrep- ancy in this non-sensitive space via the Maximum Mean Discrepancy (MMD):
+ (2NNIW00)
(A' 1|11 11 (111)
where denotes the mean representation of a subgroup of nodes.
Building on Theorem 4.2, we next analyze how represen- tation disparity influences group fairness. Theorem 4.3
4

---

FDGen: A Fairness-Aware Graph Generation Model
demonstrates that by minimizing sensitive-irrelevant rep- resentation discrepaney, we can effectively reduce group disparity in model predictions (detailed proof in Appendix).
component corresponds to a latent factor (e.g. "age", "oc- cupationn), and ii) Identifying which components capture sensitive attribute-related information and which are largely free from it.
Theorem 4.3. For a classification task, minimizing the sensifive representation discrepancy between two sensitive groups upper-bounds the group disparities:
In the first task, we aim to decompose the node embedding into multiple components, each representing latent factor. When performing this task, using all neighbors to recon- struct the node component should be avoided, as only a subset carries useful information for the specific channel. For instance, if the latent factor is "family", neighbors denot- ing close family members should have higher weight, while unrelated neighbors should be nown-weighted. To achieve such selective neighbor usage, we extend GAT-like attention into multi-channel setting via a neighbor-assigne mecha- nism. Specifically, we assume that if two nodes ey and vj exhibit higher similarity in the ch component space, then factor e is more likely to be responsible for their connection. For each channel E (1, we compute the edge weight (, between nodes e; and vj using dot-product attention to measure their similarity in channel c:
ADP
Σ f(zi), - 1
Σ {(2))) JES,
IVea ieSa
|V,,1
x ((epoos) - S(eper)))
1V8
VVs Σ
+
[Va,
|w
w (ngb !)
Based on these theoretical results, we propose a fair regu- larizer LT that reduces MMD in sensitive-irrelevan node representations while adjusting inter- and intra-group con- nections:
CT = a aly + bbg
a [Vol
Σ
0.. 5)
exp((hg,)*11) ((C)) w Wei Σ EnyEN(r.) exp( hhS,)
(4)
Byayy
+ Vsy
p
Σ
k(h
0.5
1...) In
(3) where (t;;) denote the neighbors of et. Using these edge weights (w,,,,) ) we adaptively aggregate information from relevant neighbors for each component. The aggregation process to obtain f (the tt channel representation of
eve Vay
2 [Vs
kch 03.5 h
VcCVs by CVs,
+ b (1|Emmee
A Amnerll ll.- Emntaa
Auema lF:)
node iú at layer + 1) is defined as follows:
where Lj denotes the node-level fairness term that aligns h1 across sensitive subgroups, and Lg captures the dif- g
1 o Σ (1)))
wiewee)) (Hogges Wor (5)
ference in modeling performance between inter- and intra- group edges, with a and 6 as hyperparameters that balance their contributions. In addition, Emerr and Emua denote pre- dicted inter- and intra-group connections, while Ainter and Aintra indicate their ground-truth adjacency.
where o(-) is a non-linear activation. By focusing on rel- evant neighbors in each channel, the aggregation in Equa- tion (5) encourages h(t) to cluster nodes that share similar characteristics under factor c.
In summary. L1 aims to align non-sensitive representations across different groups, while pushing the predicted graph edges to better match intra-group and inter-group statistics. Lr, integrated into FDGen, thus functions to mitigate both structural and feature biases in the generated graphs.
However, although the above mechanism decomposes the node embedding into multiple channels. it does not guaran- tee that these channels themselves mutually independent. For instance, channel e₁ "age" might still be correlated with channel c "nursing home". To address this, dis- entangled constraint which adopts a distance covariance regularizer (Matteson & Tsay, 2017) that penalizes inter- channel correlations is proposed as follows:
4.2. Identifying Sensitive-irrelevant Representations
Equipped with the proposed fairness regularizer (Section 4.1), we now present how to disentangle node representa- tions so as to isolate the components independent of sensi- tive attributes, thus enabling us to measure graph generation discrepancies and enforce fair graph generation regularizers. This process involves two main tasks: i) Decomposing each node representation into multiple components, where each
dCo, 700)
La
-= c2 dCoov 2a) (Cox Zo,)
(6)
5

---

FDGen: A Fairness-Aware Graph Generation Model
where Ne denote the number of channels and Z denotes the set of node embeddings in channel (e.g., za (htes, 1), 2)...)........... hie NN,, } and coo(-) is the distance covariance.
than merely masking edges, FDGen learns a node ordering network that, each diffusion step i, selects node ey to absorb. In an autoregressive fashion, the node decay or- dering a is sampled from q0(a | Go = (Xo. Aot), where jo Go) is a conditional probability distribution over pos- sible node orderings a. Here, Xn and Ag denote the initial node features and graph structure at time step 0. At subse- quent time steps. Xt, and A, represent the node features and graph structure after absorbing one node. This process continues iteratively until the entire graph is absorbed. To systematically select which nodes to absorb at each step, the diffusion ordering network follows a recurrent structure:
With the decomposed channels, the second task identifies which channel captures sensitive attribute information. The- orem 4.4 demonstrates that in fully disentangled representa- tions, only one channel can be associated with each sensitive attribute.
Theorem 4.4. Suppose we have channel representations fhe,,hez..... hea....,,harr ,ex,, that are fully disentangled, meaning each channel is strictly independent from every other. For- mally, I (h h = 0, i j. Then, at most one channel can capture the sensitive attribute.
gola |Go = II do (or | Go, ((t))
(8)
Hence, once we identify which channel is sensitive-related, the remaining channels can be treated as consitive-attribute independent. To this end, we train channel-level discrimi- nator that tries to predict node's sensitive label Vs. from each channel embedding. Specifically, for channel k; we feed he, into a classifier to produce the predicted probability ks.,k of the sensitive label, and define the classification loss as follows:
At each step 4, the probability of selecting or depends on the original graph Go and all previously chosen nodes (ct). We employ GNN to encode graph structure, incorporating positional encodings to represent the partial ordering. After running the GNN, we obtain an updated embedding he for each node v.. The probability of selecting the next node q0(0r Gg. ((<))) is then computed using a softmax over node emheddings:
exp(h!)
LD Σ -
Uve log(Dane) + (1 V..) log(1 Bu,e)]
(o | Go, ((()) = Σx e grren exp h?)
V2L
(7)
Through this approach, FDGen learns an ordering strategy that efficiently masks nodes during forward diffusion.
where ys. is the ground truth sensitive attribute label for node os and Us is the prediction sensitive attribute. Chan- nels that yield high classification accuracy for Ve, are deemed sensitive-related, while those with low accuracy are considered sensitive. Consequently, the fairness regularizer (Section 4.1) can be applied specifically to the sensitive-irrelevant components, ensuring minimal distribu- tional discrepancy across different groups in the generated graphs.
Reverse diffusion process: During the reverse diffusion process, our goal is to reconstruct both the node features X.) and the adjacency Ao from their noisy versions X, and A,- Specifically, let Go:n represent all the intermediate states of the graph from Gg to Gn, and let ( Go) be the forward node-decay ordering network. To this end, FDGen uses maximum likelihood estimation, which optimizes the denoising model while guiding the denoising order through variational inference, leading to higher-que quabrrr generated graphs. The variational lower bound (VLB) of the likelihood of Go is:
4.3. Fair Graph Generative Process
This section presents the proposed fair graph generative model, FDGen, which incorporates both the fairness regular- ization constraint and the disentangled conditioning mecha- nism. The overall process is divided into two stages: i) the forward diffusion process, where the graph is gradually cor- rupted to obtain noisy samples, and ii) the reverse diffusion process, where we reconstruct the graph in a fairness-awar aware and disentangled manner. We will then deseribe each part in detail:
log Pa (Go) = log ( p(Go..
(G
Go)
dG
(
Go)
2 Ey (oi.
log po
(Gr G(+1)
- KI. KI. go (o mm |Go
|| po (#1m Gn)
(10)
Forward diffusion process. During the forward diffusion process, FDGen constructs noisy versions of the input graph by successively absorbing (masking) individual nodes and their edges according to a Markov chain. Specifically, rather
Due to node permutation invariance (Kong et al., 2023). there is no need to learn a separate reverse node-generation
ordering, allowing the omission of the KL term in the varia- tional lower bound and leading to a simplified objective. The
6

---

FDGen: A Fairness-Aware Graph Generation Model
training objective (Cp). which is minimized using stochastic gradient descent, is thus defined as:
purchased together, node features are bag-of-words vectors derived from product reviews, and labels correspond the product category. Table summarizes the statistics of these datasets.
Lp - E (o (o) Σ log DogpoGG G++1)
Table I. Summary of the datasets used the experiments.
=nn -n mo (Go) Benen log po (O=(21) |
G
Dataset
Cora
Citeseer
Photo
Computer
(11)
Nodes
2,708
3,327
7,650
13,752
where t is drawn uniformly from {L...., n and Oz indicates the node Vo and its edges with any previously unmasked nodes (Te*1...., Jn).
# Edges
10.556
9,228
238.163
491,722
Features
1,433
3,703
745
767
Average Degree
3,89
2.77
31.13
35.75
While Equation 11 guides the model to learn a generative process that reconstructs node features and edges, it does not explicitly address bias nor disentanglement. To ensure fairness across different groups and decompose node repre- sentations into multiple channels (Section 4.2), for node U/ the node embedding at the 1th layer follows Equation 5.
Sensilive
Product Categorics
Product
Topic
Topic
Attribute
Categories
Baselines. We compare the proposed method with the following baselines: GRAPHARM (Kong et al., 2023), FairAdj (Li et al., 2021). FGPAN (Wang et al., 2023c), FairGen (Zheng et al., 2024) and FairWire (Kose Shen, 2024b).
Building on this, we integrate the proposed fairness con- straint into the denoising network GG: G.+1). Specifi- cally, we use f to reduce feature discrepancies among dif- ferent sensitive groups and Cy to constrain gater-group and intra-group edge biases. Hence, we augment the likelihood term in Equation 11 with these fairness and disentanglement losses. During each reverse diffusion step, the aggregator (Equation 5) updates node embeddings split by channel, and we measure fairness and disentanglement on the resulting representations. Thus, the final training objective is:
Evaluation Metrics. We evaluate FDGen's performance across two aspects: 1) Node Classification Performance: We use accuracy and F1 scores to evaluate node classifi- cation utility, along with ADP (Dwork et al., 2012) and AEO (Hardt et al., 2016) to assess prediction fairness. 2) Generated Graph Quality: Following (Kong et al., 2023), we measure generation quality using maximum mean discrep- ancy (MMD) between generated and input graphs, specifi- cally computing MMD for degree distribution and clustering coefficient. To evaluate graph structural fairness, we pro- pose metrics, fair degree distribution and fair clustering co- efficient, that measure disparity between subgroups. These are computed as: [(S,, Gs,) [ 9s,)) where s(-) denotes the MMD value for degree distribution or clustering coefficient, and 9 represents the generated graph.
Lintal Lpp + d1 bzf + A2 La AD (12)
where Lusin ensures node and edge reconstruction, C, and fg mitigate bias in node features and topology, and La with Lo enforces disentangled channels and isolates the sensitive attribute. Note that FDGen preserves 5 throughout training and sampling (i.e., S is initialized according to its original distribution at inference time) so that FDGen can capture how sensitive attributes correlate with graph structure without amplifying undesirable biases.
5.1. Experiment Results
Graph Generation Results. We evaluate our generative models in terms of both quality and fairness, with results shown in Figure 2. FDGen demonstrates strong perfor- mance in graph generation, achieving comparable or better quality than baseline methods while significantly improving fairness metrics. The strong performance can be attributed to two key factors. First, FDGen maintains group identity information through decomposition learning while reducing differences in sensitive-ireeleaat attributes. This approach enables FDGen to achieve fairness with minimal compro- mise to synthetic graph quality compared to other fairness- aware baselines. Second, by simultancously addressing both structural and feature bias, FDGen better mitigates group dif- ferences in generated graphs compared to existing methods that focus solely on structural bias. Overall, these experi-
5. Experiment
Datasets. Four real-world fairness datasets, namely Cora, Citeseer, Photo, and Computer, are used in our experiments. We provide short overview of these datasets as follows: In the Cora and Citeseer datasets (Sen al., 2008), nodes rep- resent papers, edges capture citation relationships between papers, node features are bag-of words vectors of keywords, and labels indicate the research field of the papers. The Photo and Computer datasets (Shchur et al., 2018) are seg- ments of the Amazon co-purchase graph, where nodes rep- resent products, edges show that two products are frequently
7

---

FDGen: A Fairness-Aware Graph Generation Model
1.0
1.0
0.8
0.6
0.0
0.4
0.2
0.2
02
6.0
0.0
06
0.0
00
Clks
Pat-Ckus
D0.
Clu.
NDF
Cora
Oleser Degree
Ploto
Computer
Core
Cisset
Photo Confiiient
Combutarr
Dittibbttion
Clstering
1.0
0.8
0.0
0.0
0.5
0.4
0.4
0.4
0.2
0.2
0.2
02
0.0
0.0
0.0
0.0
00:
Clis
SF 00.
Cks
00.
Clus.
Computer
Far
Car.Clus
Ceea
Closen Fwi Degiees Distribution
Photo
Combrstrr
Core
Far Clustering Coefficlemt
Cteeser
Computer
GRAPHARM
FarAd]
PGPAN
FD0mn
#DOix=WD
FaieWer
FDGm
Figure 2. Graph generation results on Cora, Citeseer, Photo and Computer datasets.
Figure 3, Ablation study results for FDGen, FDGen-WD. and FDGen-WS.
reduced graph generation quality compared the complete FDGen model. This decline in performance occurs because eliminating group identity information reduces the authen- ticity of generated graphs.
mental results demonstrate that FDGen effectively improves fairness while maintaining graph generation quality.
Table 2. Node classification results the Cora dataset.
Second, we study the effect mitigating only feature bias by creating FDGen-WS. Results in Figure show that FDGen- WS achieves worse fairness compared the complete FDGen model. While nodes may have similar censitive-irreleann attributes, their connections remain influ- enced by sensitive-related information, leading to increased connectivity between nodes sharing sensitive attributes and introducing structural bias. However, FDGen- WS main- tains better graph generation quality than FDGen-WD, Over- all, these findings underscore the necessity of our design choices.
Cora dataset
ACC (%)
Anr(%)
(%)(%)
Original-GCN
82.43 0.34
27.01 1.38
25.21 + 1.13
GRAPHARM-GCN
81.03 = 0.23
25.21 = 1.38
21.31 + 1.43
FairAdj-GCN
77.77 1.64
17.13 = 6.36
13.96 + 2.24
FGRAN-GCN
78.10 0.81
18.66 4.30
14.05 1 0.32
FairGen-GCN
79.54 1.56
14.16 0.89
13.35 1 1.24
FaiNWireGCCN
78.21 1.03
14.76 0.24
13.65 1: 0.51
FDGen-GCN
80.05 1.03
13.88
0.24
11.95 + 0.37
Node Classification Results. We evaluate both the accuracy and fairness of node classification using generated graphs. For this evaluation, we use GCN as our base model, training it on generated graphs and testing its predictive performance. Using the Cora dataset as a case study. Table shows the comparison between FDGen and baseline methods the node classification task. The results demonstrate that graphs generated by FDGen consistently lead to better classifier performance in terms of both accuracy and fairness. This improvement stems from FDGen's 's ability to mitigate both structural and feature bias during graph generation, thus re- ducing bias propagation from raw graph data to downstream tasks.
6. Conclusion
Generating synthetic graphs that capture structural charac- teristics real data has gained increasing attention as a solution to scalability and privacy challenges in real- world networks. However, fairness in graph generation models remains important yet understudied problem. This work addresses this gap by investigating bias in graph data and proposing FDGen, a framework that mitigates both struc- tural and feature bias. Our theoretically grounded fairness regularizer effectively reduces identified bias factors, as demonstrated through extensive experiments comparing FD- Gen with both fainness-agnostic and fairness-awarr base- lines real and synthetic graphs. These results establish foundation for developing fair graph generation models and open possibilities for future work on comprehensive study of graph learning.
Ablation Study. To verify the effectiveness of our proposed modules, we conduct an ablation study examining two vari- ants of FDGen. First, we analyze the impact of identifying sensitive-irrelesn representations by creating FDGen- WWD, which applies fair regularization directly to complete node representations. As shown in Figure 3, FDGen- WD shows
8

---

FDGen: A Fairness-Aware Graph Generation Model
Acknowledgements
Grover, A., Zweig, A., and Ermon, S. Graphite: Iterative generative modeling of graphs. In International confer- ence machine learning, pp. 2434-2444. PMLR, 2019.
This work was supported in part by the National Science Foundation (NSF) under Grant No. 2404039.
Hardt, M., Price, E., and Srebro, N. Equality of opportunity in supervised learning. Advances in neural information processing systems, 29, 2016.
Impact Statement
Graph generation models are increasingly used in real-world applications spanning from social networks to financial sys- tems. When these models inherit and amplify societal biases, they can perpetuate discrimination and unfair treatment of disadvantaged groups. Our work advances fairness in ar- tificial intelligence by developing methods to identify and mitigate both structural and feature bias in generated graphs. This research has particular significance for high-stakes applications such as credit scoring and healthcare, where biased graph generation could disprolpotionnatll affect vul- nerable populations. By enabling fairer graph generation while maintaining data utility, our work contributes more equitable Al systems and provides a foundation for future research structural fairness in graph learning.
Hofstra, B., Corten, R., Van Tubergen, F., and Ellison, N. B. Sources of segregation in social networks: novel ap- proach using facebook. American Sociological Review, (2(3):22-656, 2017.
Huang, H., Sun, L., Du, B., Fu, Y., and Lx, W. Graphgdp: Generative diffusion processes for permutation invariant graph generation. In 2022 IEEE International Conference on Data Mining (ICDM), pp. 201-210. IEEE, 2022.
Kang. J., Zhu, Y., Xia, Y., Luo, J., and Tong, H. Rawlsgen: Towards rawlsian difference principle on graph convolu- tional network. In Proceedings of the ACM Web Confer- ence 2022, pp. 1214-1225, 2022.
References
Kong, L.,, Cui, J., Sun, H., Zhuang, Y., Prakash, B. A., and Zhang. C. Autoregressive diffusion model for graph gen- eration. In International conference on machine learning, pp. 17391-17408, PMLR, 2023.
Akoglu, L.,, McGlohon, M., and Faloutsos, C. Rtm: Laws and recursive generator for weighted time-evolving graphs. In 2008 Eighth IEEE International Conference on Data Mining, pp. 701-706. IREE, 2008
Kose, O. D. and Shen, Y. Fairgat: Fairness- awaree graph attention networks. ACM Transactions on Knowledge Discovery from Data, 18(7):1-20, 2024a.
Bojchevski, A., Shchur, O., Zügner, D., and Günnemann, S. Netgan: Generating graphs via random walks. In International conference machine learning, pp. 610- 619. PMLR, 2018
Kose, O. D. and Shen, Y. Fairwire: Fair graph generation. arXiv preprint arXiv:2402.00 043300 2024b.
Chakrabarti, D. and Faloutsos, C. Graph mining: Laws, generators, and algorithms. ACM computing surveys (CSUR), 38(1):2-es, 2006.
Li, M., Kreačić, E., Potluru, V. K., and Li, P. Graphmaker: Can diffusion models generate large attributed graphs? arXiv preprint arXiv:2310. 13833, 2023.
Li, P., Chien, I., and Milenkovie, O. Optimizing general- ized pagerank methods for seed-expansion community detection. Advances in Neural Information Processing Systems, 32, 2019.
Chen, X., He, J., Han, X., and Liu, L.-P. Efficient and degree- guided graph generation via discrete diffusion modeling. arXiv preprint arXiv:2305.04111. 2023.
Dai, H., Nazi, A., Li, Y., Dai, B., and Schuurmans, D. Scalable deep generative modeling for sparse graphs In International conference machine learning, pp. 2302- 2312. PMLR, 2020.
Li, P., Wang, Y., Zhao, H., Hong, P., and Liu, H. On dyadic fairness: Exploring and mitigating bias in graph connections. International Conference on Learning Representations, 2021.
De Cao, and Kipf, T. Molgan: An implicit genera- tive model for small molecular graphs. arXiv preprint arXiv: (00v: 19933 2018
Li, Y., Wang, X., Ning, Y., and Wang, H. Fairlp: Towards fair link prediction social network graphs. In Proceed- ings of the international AAAI conference on web and social media, volume 16, pp. 628-639, 2022.
Dwork, C., Hardt, M., Pitassi, T., Reingold, O., and Zemel, R. Fairness through awareness. Proceedings of the 3rd innovations in theoretical computer science conference, pp. 214-226, 2012.
Liu, J., Kumar, A., Ba, J., Kiros, J., and Swersky, K. Graph normalizing flows. Advances in Neural Information Pro- cessing Systems, 32, 2019.

---

FDGen: A Fairness-Aware Graph Generation Model
Liu, Q., Allamanis, M., Brockschmidt, M., and Gaunt, A. Constrained graph variational autoencoders for molecule design. Advances in neural information processing sys- tems, 31, 2018.
Conference on Data Mining (ICDM), pp. 638-63887777 IEEE, 2023a.
Wang. Z., Saxena, N., Yu, T., Karki, s., Zetty, T., Haque, I., Zhou, S., Kc, D., Stockwell, I., Bifet, A., et al. Preventing discriminatory decision decision-making in evolving data streams. In Proceedings of the 2023 ACM Conference on Fairness, Accountability, and Transparency (FAceT), 2023b.
Matteson, D. S. and Tsay, S. Independent component analysis via distance covariance. Journal of the American Statistical Association, 1 112(518))623-633 2017.
Niu, C., Song, Y., Song. J., Zhao, S., Grover, A., and Ermon, S. Permutation invariant graph generation via score-based generative modeling. In International Conference on Ar- rificial Intelligence and Statistics, pp. 4474 4484. PMLR, 2020.
Wang. Z., Wallace, C., Bifet, A., Yao, X., and Zhang, W. Fg an: Fairness-awarr graph generative adversarial net- works. In Joint European Conference on Machine Learn- ing and Knowledge Discovery in Databases, pp. 259-275. Springer Nature Switzerland, 2023c
Rahman, T., Surma, B., Backes, M., and Zhang, Y. Fairwalk: Towards fair graph embedding. 2019.
Wang, 7., Chu, Z., Blanco, R., Chen, 7.,, Chen, S.-C., and Zhang, W. Advancing graph counterfactual fairness through fair representation learning. In Joint European Conference Machine Learning and Knowledge Dis- covery in Databases, pp. 40-58. Springer Nature Switzer- land, 2024a.
Sen, P., Namata, G., Bilgic, M., Getoor, L., Galligher, B., and Eliassi-Radd Rad, T. Collective classification in network data. magazine, 29(3):93-93, 2008.
Shchur, O., Mumme, M., Bojehevski, A., and Günnemann, S. Pitfalls of graph neural network evaluation. arXiv preprint ar arXiv: 1.10088 2018.
Wang, Z., Qiu, M., Chen, M., Salem, M. B., Yao, X., and Zhang, W. Toward fair graph neural networks via real counterfactual samples. Knowledge and Information Sys- lems, pp. 1-25, 2024b.
Shumovskaia, V., Fedyanin, K., Sukharev, I., Berestnev, D., and Panov, M. Linking bank clients using graph neural networks powered by rich transactional data: Extended abstract. In 2020 IEEE 7th International Conference on Data Science and Advanced Analytics (DSAA), pp. 787-788, 2020.
Wang. Z., Ulloa, D., Yu, T., Rangaswami, R., Yap, R., and Zhang, W. Individual fairesss with group constraints in graph neural networks. In 27th European Conference on Artificial Intelligence, 2024c.
Simonovsky, M. and Komodakis, N. Graphvae: Towards generation of small graphs using variational autoencoders. In Artificial Neural Networks and Machine Learning- ICANN 2018: 27th International Conference on Artificial Neural Networks, Rhodes, Greece, October 4-7, 2018, Proceedings, Part 1 27, pp. 412-422 Springer, 2018.
Wang, Z., Chu, Z., Viet Doan, T., Wang. S., Wu, Y., Palade, V., and Zhang, W. Fair graph u-net: A fair graph learning framework integrating group and individual awareness. In proceedings of the AAAI conference on artificial intel- ligence, volume 39, pp.
2025a
Sohl-Dickstein, J., Weiss, E., Maheswaranathan, N., and Ganguli, S. Deep unsupervised learning using nonequi- librium thermodynamics. In International conference on machine learning, pp. 2256-2265. PMLR, 2015.
Wang, Z., Hoang, N., Zhang, X., Bello, K., Zhang, X., Iyen- gar, S. S., and Zhang, W. Towards fair graph learning without demographic information. In The 28th Interna- tional Conference on Artificial Intelligence and Statistics, 2025b.
Wang, X., Hc, X., Wang. M., Feng, F., and Chua, T.-S.
Neural graph collaborative filtering. In Proceedings of the 42nd international ACM SIGIR conference on Research and development in Information Retrieval, pp. 165-174, 2019.
Wang. Z., Liu, F., Pan, S., Liu, J., Saced, F., Qiu, M., and Zhang, W. fairgnn-wod: Fair graph learning without complete demographics. In Proceedings of the 34th In- ternational Joint Conference on Artificial Intelligence, 2025c.
Wang, Z. and Zhang, W. Group fairness with individual and censorship constraints. In 27th European Conference on Artificial Intelligence, 2024.
Wang, Z.,, Wu, A., Moniz, N., Hu, S., Knijnenburg, B., Zhu, X., and Zhang, W. Towards fairness with limited demographics via disentangled learning. In Proceedings of the 34th International Joint Conference on Artificial Intelligence, 2025d.
Wang, Z., Narasimhan, G., Yao, X., and Zhang, W. Miti- gating multisource biases in graph neural networks via real counterfactual samples. In 2023 IEEE International
10

---

FDGen: A Fairness-Aware Graph Generation Model
Wang, Z., Yin, Z., Yang, L.., Zhuang, J., Yu, R., Kong, Q. and Zhang, W. Fairness-aware graph representation learn- ing without complete demographic information. In Joint European Conference on Machine Learning and Knowl- edge Discovery in Databases. Springer Nature Switzer- land, 2025e.
Zhang, W., Wang, Z., Kim, J., Cheng, C., Oommen, T. Ravikumar, P., and Weiss, J. Individual faimess under uncertainty. In 26th European Conference Artificial Intelligence, pp.
2023b
Zhang, W., Zhou, S., Walsh, T., and Weiss, J. C. Fairness amidst non-iid graph data: A literature review. Al Maga- zine, 46
Wang, Z., Yin, Z., Yap, R., and Zhang, W. Ai fairness beyond complete demographics: Current achievements and future directions. In 28th European Conference Artificial Intelligence, 2025f.
1 1 12112, 2025.
Zheng, l.., Zhou, D., Tong, H., Xu, J., Zhu, Y., and He, J. Fairgen: Towards fair graph generation. In 2024 IEEE 40th International Conference on Data Engineering (ICDE), pp. 2285-2297. IEEE, 2024.
Wang. Z., Yin, Z., Yap, R., Zhang, X., Hu, S., and Zhang, W. Redefining fairness: A multi-dimmnnional perspective and integrated evaluation framework. In Joint European Con- ference Machine Learning and Knowledge Discovery in Databuses. Springer Nature Switzerland, 2025g.
Zhu, Y., Li, J., Bian, Y., Zheng, Z., and Chen, L. One fits all: Learning fair graph neural networks for various sensitive attributes. In Proceedings of the 30th ACM SIGKDD Conference Knowledge Discovery and Data Mining, pp. 4688-4699, 2024.
Wang, Z., Yin, Z., Zhang, Y., Yang. L., Zhang, T., Pissinou, N., Cai, Y., Hu, S., Li, Y., Zhao, L., et al. Fg-smote: To- wards fair node classification with graph neural network. ACM SIGKDD Explorations Newsletter, 26(2):99-10) 108, 2025h.
You, J., Liu, B., Ying, Z., Pande, V., and Leskovec, J. Graph convolutional policy network for goal-directed molecu- lar graph generation. Advances in neural information processing systems, 31, 2018.
Yu, H., Sun, X., Solvang, W. D., and Zhao, X. Reverse logistics network design for effective management of medical waste in epidemic outbreaks: Insights from the coronavirus disease 2019 (covid-19) 19) outbreak in wuhan (china). International journal of environmental research and public health, 1775)17770 2020.
Zhang, G., Cheng, D., Yuan, G., and Zhang, S. Learn- ing fair representations via rebalancing graph structure. Information Processing & Management, 61(1):103570, 2024.
Zhang, W. Ai fairness practice: Paradigm, challenges, and prospects. Ai Magazine, 45(3):386-33 3906663355010 2024.
Zhang, W. and Ntoutsi, E. Faht: adaptive faimess-awan decision tree classifier. In Proceedings of the 28th Inter- national Joint Conference on Artificial Intelligence, pp. 1480-1486, 2019.
Zhang, W. and Weiss, C. Longitudinal faimess with censorship. In proceedings of the AAAI conference on tificiall intelligence, volume 36, pp. 12235-12243, 2022.
Zhang, W., Barraandz--Boussaee T., and Weiss, J. Cen- sored faireess through awareness. In Proceedings of the AAA/ conference on artificial intelligence, volume 37, pp. 1461 14619,, 2023a.

---

FDGen: A Fairness-Aware Graph Generation Model
A. Proof of Theorem 4.2
To simplify the notation, we use h' to denote the input representations, and h + to denote the output representations. The considered disparity measure follows as:
( SD
MMD ( E Vsal, (hs vs E Vss))
(13)
Expand under the RBF kernel function: k(x,, v) exp (->|1> y)1²), we can get:
(1) hgD
Σ
Σ
Ah h2s))
2 [Val
h h n1ss)) (14)
Vs
Vs,
VVs,
We Vsa eyeVs
Building on this, and given that Graph Attention Networks (GAT) adopt the message passing by assigning different weights to neighbor nodes as:
(1-1) exp (111)
h
Σ
dig
a-1)
with
dij
(15)
E EeyEAr()) exp (0)-1)
Hence, we can re-write the disparity as follows:
h 11
=X
Σ
aiu h (1-1)
(11) (-1)
Σ
aiu
(111)
(--thh!" h!!1)
aEAinSa
WEWinSy
Kh 1111) (1-1)) h 11) + NaN
h
Σ
Wh (h(1-1) h (1-1)) h ((-1))
N3
(16)
WES
WES,
Σ MESA
Mh b 1- N&N
1(h (1-1) h (1-1) h (1-1)
uES,
Given that each node E Sá. the node representation 1 subject to (((0) A 11 3 pr (d) A' (Kose & Shen, 2024a), where the parameter A' serves per-layer tolerance indicating how far the representation is allowed to deviate from μ (d) along each coordinate. If u instead belongs to Sy, a parallel condition applies with p.!") A anchoring h! around the group mean p. (/) Building this, assume the node representation within controlled region near its respective group's mean. Hence, we can define the h." as:
h
((d)+
+
Σ
1 n(-1)
(--1
uEAinSa
WENinS
Σ
l (h! (1-1)
h 11-1) + NaN wES;
Σ k(h (-1), h )
N2
Σ (h (1-1) (1- 1 (-11) NaN,
Σ (h( h 11 ( 19
WES.
wES,
+ 2 N W b0 A +
11 14 11)]]]]]
Building on this, for nodes v E S4, we have:
12

---

FDGen: A Fairness-Aware Graph Generation Model
1 Σ -n E ula) + (ui +
- (1fi--
a-
aj
Na SESa
Nd
SeSa
Σ Σ
(d) - 21 1)] Knn nng 1) (1/_) -1) + |2/N// (A'+ (A'+1l4
N2 1
iESa WES;
We can do similar for Sy.
1
In
(12
Σ
oj (1i-1 - m)2))
(1 (d)
(14
1 jES,
Ns jES;
Σ
Σ
Kh!l n, 1) (11=1 - m1 + // 1150 (A' + +11
1 D]]
+
Na N7
JESy uESa
(18)
We define the upper bound of the consequent representation discrepancy on node representation between two sensitive groups as follows:
1
h
Σ
n
=
No
VESa
JESy
$ 1 -
1
Σ
Σ
diu
(11)
+ Nj
1 Σ Σ
a3s ")
NA
iES, u NEN, (vi)
jeS,
(15)
Σ
Σ
Kh
(1-1 ,
h ((ال
||019 1
N7 + N₃N,
VES
+ |nla) - -loii|
10
|1 (A'
+
11/0) 1]]
< No Σ Σ
dia (1-))) + , Σ Σ
auu d(t +1
(19)
iES WENinSepp (15)
5E WEN, (up
Mh! (111) (h(l11) h (111) |1(-0
(1
No + NgN,
JES,JES;
+ (2)a0 - + [2V/NII 1100 (A' + || (1) 11]
S (3 (MaNy N
Σ Σ Kh!!- , bn(-1)) )) || | - 14
SESaJES,
+ ||00000 - + +2VVNi ao (A' + || (d) u4 (211) I)]
Noting that each node representation h, can be decomposed as h, = hig @ hy: (sensitive vs. non-sensitive part), we obtain the analogous upper bound for the sensitive-irelleant representation h Hence, the representation discrepancy between different sensitive groups in the non-sensitive subspace is also bounded by:
h ()) S.D
5(3
S 3 - VV.. IV
+
1
Σ
k(hb 1(5))) |1 - -1-ill + || - 10
Vs,
Vvs.
iESA,JES,
(00)
+ /2/N// (A' - -1((/0 14/ (111]]]]
which concludes the proof.
13

---

FDGen: A Fairness-Aware Graph Generation Model
B. Proof of Theorem 4.3
For binary classification, statistical parity is defined as: Asp = PP = 0) P(ú 1/s = 1)1. We consider the binary classification task and examine the properties of the Softmax function this context. Let P1 and P2 represent the probabilities of class 1 (ct) and class (c2), respectively. The function Softmar(-)) is Lipschitz continuous with Lipschitz constant L. Due to this Lipschitz continuity, the difference in output probabilities can be bounded by the difference in input vectors:
[l5();) - /(hy))l = PP: P21 + (1 P3) (1 P1)
(21)
2 P1 P3 - L h hyll
where h; is the node representation for Vu; E Sa and hj is the node representation for Vez E Sz. Building this, rewrite the statistical parity follows:
ADP
1 Na ieSa
Σ f(z)),
E(1))
(22)
N₁ JES,
where z, = w'n and W1() is the weight matrix at layer As we discuss above, from Equation 21 and using node on from the group Sa an example, we can get:
f(,) f(2200011 S
L L||z 2ntel |I
(23)
Therefore, rewrite it as:
1 1|2 - -2,001 $ s(a), 1 (( + $ f112 2 I (2
(24)
Let z, = h (9) for node i, and 2 = w1) 240 = w() ( be the group means in logits space.
Nu
N Σ
f(zu(a))1 f(zn(t))1 No Σ
1lzz
1
Izz
N
==1
f(zi) - 1
Σ
f(z;)1 z
No IES,
jES,
Na
N; N₁
f( f(z,(o)) - f(z,(1))1
1
Σ
2/2
l|zz
2,000
1 +
l|z - 1a01
Consider the hn obtained:
|z, - = (w(0 - (
|| (3- NNNy + NGN,
Σ Σ 1ah ((h
b((11)) |1 - 112111
(25)
SESa SE
+ (11 - -1011 + (2V (A' 11 14 -1 [111
and we can get similiar for ||z. - znin
14

---

FDGen: A Fairness-Aware Graph Generation Model
Building on this, we re-express the upper bound.
ADP
1
Σ f(zi)1
Σ EE f(2z)1
1
Na
Ns jES,
iESa
(26)
Na
N₂
+
1.
Σ
z
2 ll +
1
Σ
2g
z
Na
Here we have combined the group center difference [f(2)()) - f(zuen))] with the Lipschitz offset 1 , 1zz - znin Il. factoring out 4.
E I|, - 2 +
Na
We note that
12 p || = | (h. (n(
)1)) $ | (n4h) (1
(27)
Similarly for x, 2000 According to (I), we know
[n (010 || S (3 NaN3 N3N,
Σ Σ
(hn (1 (((--),n((-1)) ) |11f-11
12
(28)
PESa DES,
+ (l - ااا1 + [2/N]/
(A' 1++11e [1'+1mm 111 -11 11]
By Theorem 4.2, ||b!" ())
ui (d) itself bounded by a term involving ||x/-1 - (D plus L (| and C/ Thus,
I|z |,100 ||
< || [33 (3-(NNiNg
No NYN,) Σ Σ ((n(-1),n(11))
n((111))) 1 11-1
(29)
9ES,
+ [1 - || + [2VIN (A' + || (10)
m (5) [)]
Similarly for [|z 2/ Plugging these bounds into (24) and summing over es Sa, Bj E S yields:
APP 1 [f(z)(0) f(zm(n))l
N4
+ ト/ |
(3 No + NęNN)
Σ k(h(-1) (1-1) h (()-))) || - 1121l
P-8
(1|p((0) 11011 + 12VN A + 11 (1111]
(30)
N2
Σ
(3 NoN + N
==l
Σ k(n (11-))) 111 - -22211
P-2
(l(p(1) - 11011 (2VT (A' + 1144 ( - -4, (111)
We can rewrite as:
15

---

FDGen: A Fairness-Aware Graph Generation Model
APP
Σ
f(zi)1
Σ JES,
f(2z))
Nd iESa
Nj
No
N + N7
(2 - M(nesss1
+ 2
No
2i
2
22 - (ncss11)
==1
j=1
Na
Nj
(31)
< f(zwia)) - f(zuer))
+ L
1gD
(1)
+ N
w
bgD (3)
Na
f(zplo)) f(zu(r))2
Na
+
N1
Na
Ns
((zntt)) - [(zn()))
L. |[
hgD
(1)
Building on this analysis, we can derive an upper bound for the bias caused by sensitive-ireelevntt node representations disparity.
App =
Σ (2i) - 1 Σ f(3)))
Vsg
[Vs,
IESa
JES,
x ((2),00)1 - f(zn(r))
(32)
IVagl
Vsy
+
L
2
Vsal
|w (1) + [Vsy
1
Σ
|
(1)
I !1)
1=1
1=1
This completes the proof.
C. Proof of Theorem 4.4
Assume there exist two distinct channels he, and he, + j) that both encode the sensitive attribute S. That is. ((h*; and 7(h O.
Hence, we can write
h
fi(S) ex h [5(8) + ej
(33)
for some non-trivial functions f:(-). J5() and noise terms E;, Ej.
Because both channels depend on S, we have
T(h h9) T(J(()) ex; [5( + Eg) T(A(S): (2S)) > 0
(34)
which contradicts the independence assumption 7(h:; he) = 0.
Therefore, under the requirement that all channels remain mutually independent, at most one channel can capture S.
D. Experimental Settings
Baselines
We compare FDGen with five lfte-of-the-art methods: performance-driven GRAPHARM (Kong et al., 2023) and fairness- aware models including FairAdj (Li et al., 2021), FGPAN (Wang et al., 2023c), FairGin (Zheng et al., 2024), and FairWire (Kose& & Shen, 2024b). A brief overview of these baselines is as follows:
GRAPHARM: GRAPHARM an autoregressive crttusion-bbsedd model for graph generation that directly operates in the discrete graph space by sequentially masking one node and its edges until the graph is empty. employs learned
16

---

FDGen: A Fairness-Aware Graph Generation Model
node ordering strategy for accurate likelihood approximation and achieves faster generation than existing graph diffusion models by limiting the number of diffusion steps to the number of nodes in the graph.
FairAdj: FairAdj updates the normalized adjacency matrix to better satisfy dyadic fairness, which requires that link predictions be independent of the sensitive attributes from both vertices. This approach lessens the statistical gap between intra-group and inter-group link predictions while preserving as much predictive accuracy as possible.
FGAAN is a fair graph generative model that addresses both node-level and structural faimess in creating synthetic graphs through adversarial training. introduces tailored faimeess metrics and a meta-strategy that reduces computational costs while handling multiple types of bias in the data.
FG²AN:
FairGen: FAIRGEN is a deep generative model that integrates label guidance and faimesss objectives to produce synthetic graphs under limited labeled data. It uses a self-paced learning strategy and novel context sampling approach to progressively learn the behaviors of protected and unprotected groups while preserving class memberships.
FairWire: FairWire is diffusion-based fair graph generation framework that uses faimess regularizer, to reduce structural bias in link prediction and synthetic graph creation. It captures the connections between synthetic sensitive attributes and the graph topology, allowing fair model training without revealing real sensitive data.
17


Reviews:
[{"review_id": "dSbtH5yie8", "reviewer": "Reviewer_sM9W", "summary": "The authors propose a diffusion-based framework for fair graph generation that addresses both structural bias and feature bias within the generated graphs. Guided by theoretical analysis, which identifies how biases arise in the generation process, the framework applies a novel fairness regularizer to disentangle legitimate group differences from unfair biases, thereby preserving graph quality while ensuring fairness across different demographic groups. In an experimental study using four common graph datasets and five baseline methods, their approach improves fairness performance while maintaining generation quality.", "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": "We sincerely appreciate Reviewer sM9W's thorough review and have provided detailed responses below.\n\n**Pre-defined sensitive attributes:** Our approach follows the standard convention in fairness research where sensitive attributes are predetermined based on legal frameworks and specific application contexts. In practice, sensitive attributes are typically defined by anti-discrimination laws (such as race, gender, age, and disability status under various civil rights regulations) or domain-specific ethical guidelines. For instance, in financial applications, factors like race and gender are legally protected categories, while in healthcare, additional attributes like genetic information may be considered sensitive. Our method is designed to work with these established definitions while remaining flexible enough to accommodate different sensitive attributes as required by specific applications. This assumption is consistent with most fairness literature in machine learning, as addressing the broader question of which attributes should be considered sensitive falls outside the scope of our technical contribution and belongs to legal and ethical domains.", "claims_and_evidence": "Yes.", "methods_and_evaluation_criteria": "Yes.", "theoretical_claims": "The theorical proof is provided in the appendix.", "experimental_designs_or_analyses": "Yes, it would be better to provide anonymous code.", "relation_to_broader_scientific_literature": "The paper builds upon prior work in fair graph learning and generative models by extending fairness research beyond structural bias to include feature bias, offering a theoretical analysis of bias propagation in graph generation and proposing FDGen as a novel mitigation approach.", "essential_references_not_discussed": "No", "other_strengths_and_weaknesses": "1. The paper addresses an important yet often overlooked fairness challenge: feature bias in graph generation, providing well-motivated reasoning for its significance in real-world graph learning applications. \n\n2. The theoretical analysis formally defines both feature and structural biases in node representations, offering analytical insights into how these biases propagate through graph generation processes.", "other_comments_or_suggestions": "1. This paper assumes that sensitive groups are clearly defined beforehand, but in practice, determining which attributes should be considered sensitive can be ambiguous and context-dependent.\n\n2.  It would be better to provide anonymous code.", "questions_for_authors": "N/A", "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": "2DJzdOAFoc", "reviewer": "Reviewer_LnUo", "summary": "The authors address fairness in graph generation problems, where fairness is meant as a trustful replication of the original graph that can then be used to train ML algorithm for automated decision making (e.g. credit scores). Their algorithm takes into account fairness both at the feature level and at the structural level. The authors designs a new fairness cost function that their algorithm minimizes.", "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": "We appreciate Reviewer LnUo's thoughtful feedback and have provided responses below.\n\n**If you need to have access to the original graph why don't you directly use it for training? And if not, how can you replace it?** \nThe original graph is not always suitable for training, so the generated graph is used instead. For example, in many real-world applications, organizations (like banks) possess valuable data but cannot directly share it due to privacy regulations. By generating synthetic graphs that preserve important information, we enable broader use of graph insights while maintaining privacy. Moreover, original graphs contain inherent biases. By using the original graph as input but applying our fairness constraints during generation, we create alternatives that reduce biases while maintaining utility, preventing discriminatory decision-making.\n\n**Selected datasets are fairness irrelevant.** \nThe selected datasets are fairness relevant and widely used in fair graph research including fair graph generation. Specifically, citation networks (e.g., Cora and Citeseer) exhibit bias where papers from certain fields have higher visibility. For example, research on diseases predominant in white populations may receive more citations than equally important research on conditions affecting African American populations. Similarly, Amazon co-purchase networks (e.g., Photo and Computer) contain structural biases where purchase patterns can perpetuate stereotypes. For instance, if certain demographic groups historically purchase products associated with higher credit scores, individuals with different purchasing patterns may receive lower scores despite being financially responsible. In summary, due to the fairness relevance of these datasets, they have been widely adopted in fairness literature [1,2], including in our work.\n\n[1] Dong, et al. \"Fairness in graph mining: A survey.\" TKDE 2023.\n\n[2] Zhang, et al. \"Fairness amidst non‐IID graph data: A literature review.\" AI Magazine, 2025\n\n**Why is fairness important in generative models?** Fairness in generative models, particularly in the context of graph generation examined in this paper, is critically important; our work is motivated by the fact that synthetic graphs directly influence high-stakes decision-making across domains such as credit scoring. As shown in our toy example in Figure 1, unfair generation can amplify biases through structural bias (connections within the same sensitive groups) and feature bias (attribute disparities across groups). For instance, biased graphs can lead to biased loan approvals when male nodes are generated with higher income values or denser financial relationships. Without addressing both bias types, synthetic graphs replicate or even amplify bias, disadvantaging deprived groups in downstream applications.\n\n**Shouldn't the matrix A be in the graph definition as well?** The adjacency matrix A and edge set E are equivalent representations. Edge sets are more storage-efficient for sparse graphs. A 10,000 node graph would require 100 million matrix entries despite having only thousands of edges. Therefore, we define G={V,E,X}.\n\n**The difference between y and s.** s refers to sensitive attributes (e.g., gender), while y denotes node labels for downstream tasks (such as loan approval decisions).\n\n**Important is not a mathematical rigorous concept, rather define it in terms of \"steps away\" from the node?** \nImportant in our work is mathematically defined through an importance score, which is based on both proximity and connection strength, rather than simply \"steps away\" from the node; Simply using steps away to build an ego graph may ignore truly important nodes or include too much noise information. \n\n**Theorem 4.4 is an assumption rather than a theorem and no proof.** \nTheorem 4.4 is a theorem rather than an assumption and here is the proof for reference.\n\n**Notations:** Let $h \\in \\mathbb{R}^{d}$ be node representation with channels $h = [h^{c_1},...,h^{c_N}]$. $I(\\cdot)$ is mutual information; $I(X;Y)=0$ means independence.\n\n**Proposition.** For all $i \\neq j$ with $I(\\mathbf{h}^{c_i}; \\mathbf{h}^{c_j}) = 0$, at most one channel can capture information about $S$. \n\n**Proof.** By contradiction. Assume at least two distinct channels $\\mathbf{h}^{c_i}$ and $\\mathbf{h}^{c_j}$ both capture information about $S$: $I(\\mathbf{h}^{c_i}; S) > 0$ and $I(\\mathbf{h}^{c_j}; S) > 0$. Then $\\mathbf{h}^{c_i} = f_i(S) + \\boldsymbol{\\varepsilon}_i$, $\\mathbf{h}^{c_j} = f_j(S) + \\boldsymbol{\\varepsilon}_j$ for nontrivial functions $f_i$, $f_j$ and noise terms $\\boldsymbol{\\varepsilon}_i$, $\\boldsymbol{\\varepsilon}_j$. Since both depend on $S$, $I(h^{c_i}; h^{c_j}) = I(f_i(S) + \\varepsilon_i; f_j(S) + \\varepsilon_j) \\geq I(f_i(S); f_j(S)) > 0$, contradicting $I(\\mathbf{h}^{c_i}; \\mathbf{h}^{c_j}) = 0$. Thus, at most one channel can capture information about sensitive attribute $S$.", "claims_and_evidence": "yes", "methods_and_evaluation_criteria": "I feel I am missing something fundamental there.\nReferring to section 4.3:\nYou need the original graph as input to the algorithm and then you produce a synthetic graph with is \"fair\" in the sense that you can faithfully replicate the feature and structural characteristics of the input. But if you need to have access to the original graph why don't you directly use it for training? And if not, how can you replace it?", "theoretical_claims": "No", "experimental_designs_or_analyses": "The authors validate their algorithm over graphs which are totally irrelevant for this methodology. I would have expected some social network topology or something more related to social settings in the field of credit score and health. Instead they use datasets about amazon products or about paper citations.", "relation_to_broader_scientific_literature": "I think in principle the problem is very important, namely how to avoid that graphs used for training ML algorithm are not biased against vulnerable communities which is very fundamental for credit score, health, etc.", "essential_references_not_discussed": "To the best of my knowledge there are not missing references", "other_strengths_and_weaknesses": "Strength: relevant and novel work\n\nWeaknesses: I am missing something fundamental, please refer to the \"input graph\" comment. \n-The algorithm should be tested on more pertinent networks where the feature and structural biases are more clear", "other_comments_or_suggestions": "Section 2.2, at the end you mention\"However fairness remains unexplored in synthetic graph generation limiting these models'use in high stake scenarios\": this is not exactly the motivation on why one should study fairness. I invite the authors to elaborate more on the importance of fairness when it comes to graph generation and bring more concrete examples on why fairness is important\n\nIn the notation:\n\nShouldn't the matrix A be in the graph definition as well? Namely $\\mathcal{G}(\\mathcal{V}, \\mathcal{E}, X, A )$. Also, it is not clear to me what the difference between y and s is. Finally, \"which includes \\textbf{important} neighbor nodes of the central node\", important is not a mathematical rigorous concept, rather define it in terms of \"steps away\" from the node?\n\nTheorem 4.4 Reads more as an assumption than a theorem, indeed there is no proof for it", "questions_for_authors": "-You need the original graph as input to the algorithm and then you produce a synthetic graph with is \"fair\" in the sense that you can faithfully replicate the feature and structural characteristics of the input. But if you need to have access to the original graph why don't you directly use it for training? And if not, how can you replace it?", "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": "9yCnt13ccF", "reviewer": "Reviewer_NfyT", "summary": "This paper proposes FDGen, a fairness-aware graph generation model that mitigates both structural and feature biases by introducing a fair regularizer and a diffusion-based framework to ensure fairness while preserving graph generation quality. Experiments on four real-world datasets show that FDGen outperforms SOTA methods in fairness and generation utility.\n\n## update after rebuttal", "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": "We sincerely thank Reviewer NfyT for the detailed review and positive assessment of our work. We are particularly grateful for your recognition that FDGen is, to your knowledge, the first work addressing feature bias in graph generation, this was indeed a primary motivation for our research. We appreciate your thorough evaluation of our theoretical claims and experimental results, confirming the technical soundness of our approach in addressing both structural and feature biases. Your acknowledgment of our work's contribution to bridging an important gap in fair graph generation research is encouraging. We will improve the clarity of figures and font sizes as suggested. Thank you for recognizing the broader impact of our work in advancing fairness in graph generation models.", "claims_and_evidence": "This paper addresses an important problem in graph generation where both structural and feature biases can propagate through generated graphs and lead to unfair downstream decisions. Although fair graph generation has been studied previously, to my knowledge, this work is the first to address feature bias in the graph generation task, presenting a well-motivated approach with a solid theoretical foundation. It bridges the gap in existing fair graph generation research, which has primarily focused on structural bias.", "methods_and_evaluation_criteria": "The proposed approach is technically sound. The fair regularizer effectively captures both feature and structural bias, while the diffusion-based generation framework maintains graph properties. The authors provide formal theoretical analysis with proofs, and their experiments on four diverse real-world datasets demonstrate consistent improvements across multiple fairness and quality metrics.", "theoretical_claims": "I checked the theoretical claims and mathematical proofs, particularly regarding the fair regularizer and bias analysis in graph generation. The derivations are logically structured and well-motivated. While the proofs appear technically sound, additional clarification of underlying assumptions would strengthen their validity and applicability.", "experimental_designs_or_analyses": "I checked the experimental design and analyses for fairness and generation quality evaluations across four real-world datasets. The experiments are well-structured, and the results support the paper's claims. However, the clarity of the pictures and font size needs to be further improved.", "relation_to_broader_scientific_literature": "The paper advances the field of fair graph generation. The related work includes necessary and recent studies, covering fairness in graph learning and generative models. To my knowledge, this appears to be the first work addressing feature bias in graph generation. The paper extends prior research by tackling both structural and feature biases, offering a novel perspective on multi-source bias mitigation in graph generation.", "essential_references_not_discussed": "Please refer to my comments above.", "other_strengths_and_weaknesses": "Please refer to my comments above.", "other_comments_or_suggestions": "None", "questions_for_authors": "Please refer to my comments 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": "0XEht2hy2d", "reviewer": "Reviewer_Pk2M", "summary": "The authors propose FDGen a novel method for fair graph generation. The authors investigate the bias sources in graph generation, then consequently define regularization terms to promote fair graph generation by mitigating both the structural biases and node feature biases.\n\n## update after rebuttal\nMy main concern regarding the very limited empirical gains of the proposed method remains valid. Figures 2 and 3 clearly highlight this issue. Therefore, I am maintaining my original score.", "questions": "", "limitations": "", "rating": 2, "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": "We thank Reviewer Pk2M for the time and thorough review. Below are our detailed responses:\n\n**The proposed method performs roughly similar to comparison methods across all metrics and benchmark datasets.**\nOur proposed method outperforms baselines with dissimilar performances. Specifically, in the graph generation tasks, the fair graph generation metrics, e.g., Fair-DD and Fair-Clus, consistently show our method performing better across all datasets. Our method achieves at least 10% improvement in fairness metrics across all four datasets compared to the baselines, with the most significant improvement of 25% on the Photo dataset. These improvements are achieved while maintaining comparable performance on quality metrics, e.g., DD and Clus. In addition, in downstream node classification tasks, our results also demonstrate substantial improvements. Compared to the worst fairness-aware baselines, our FDGen-GCN achieves a 25.61% improvement in fairness metrics. Even compared to the best baseline in fairness metrics, FDGen-GCN still achieves a 10.49% improvement in EO metrics. Moreover, compared to other fairness-aware baselines, these fairness gains come with 48.92% less accuracy loss, demonstrating our method's superior fairness-utility trade-off.", "claims_and_evidence": "Yes, the claims made in the submission supported by clear and convincing evidence.", "methods_and_evaluation_criteria": "The proposed methods and evaluation criteria make sense for the problem at hand.", "theoretical_claims": "Yes, theoretical claims and derivations seems sound to me.", "experimental_designs_or_analyses": "The experimental designs or analyses are sound.", "relation_to_broader_scientific_literature": "The work is very relevant to the scientific literature. The theoretical derivations and investigations present valuable insights to the fair graph generation task.", "essential_references_not_discussed": "Essential related works are discussed and compared against.", "other_strengths_and_weaknesses": "I greatly appreciate the insights provided by the theoretical derivations. \nMy main concern is that the experimental results show that the proposed method performs roughly similar to comparison methods across all metrics and benchmark datasets. The fact that the insights of the theoretical derivations which inspired the design choices of FDGen did not translate into empirical gains against other graph generation methods which do not consider node feature biases is the main weakness of this work.", "other_comments_or_suggestions": "N/A", "questions_for_authors": "N/A", "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 introduces FDGen, a fairness-aware graph generation model that mitigates both structural and feature biases through the integration of a fairness regularizer and a diffusion-based generation framework. A key contribution lies in the theoretical analysis that formalises how biases emerge and propagated in the graph generation process and provides analytical tools to disentangle legitimate group differences from unfair biases. This enables the model to preserve graph quality while improving fairness across demographic groups.

The theoretical contribution is well recognised and appreciated by all reviewers, particularly the formal definition and propagation analysis of structural and feature biases in node representations. These insights add significant value to the growing body of work at the intersection of fairness and generative models.

However, reviewer opinions diverged on the empirical results. Additionally, reviewers noted that parts of the paper—particularly the core methodology and technical formulation—could benefit from clearer exposition to ensure accessibility for a broader audience, especially those less familiar with fairness-aware graph learning.
Decision: Accept (poster)