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Fairness-Aware Network Embeddings: Methods, Applications, and Challenges
Ella Has, Harshith Kumar Yadav, Gaurav Dixit, Mykola Pechenizkiy, Akrati Saxena
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Summary
This survey paper reviews fairness-aware network embedding methods, proposing a taxonomy based on underlying embedding approaches (spectral, random walk, GNN, Bayesian, method-agnostic), fairness intervention strategies (pre-processing, in-processing, post-processing), and fairness objectives (embedding-level vs. task-level). It discusses challenges such as structural inequalities, homophily, and demographic imbalances, and compares methods regarding group vs. individual fairness and sensitive attribute availability.
Entities (23)
Relation Signals (10)
Network Embedding → supports → Node Classification
confidence 95% · Network embedding methods learn low-dimensional representations of graph-structured data to support downstream tasks such as node classification
Network Embedding → supports → Link Prediction
confidence 95% · Network embedding methods learn low-dimensional representations of graph-structured data to support downstream tasks such as ... link prediction
Fairness-Aware Network Embedding → mitigates → Bias
confidence 94% · fairness-aware network embedding methods have been proposed to mitigate bias while preserving embedding utility
Homophily → causes → Structural Inequalities
confidence 93% · Another major source is homophily ... Homophily leads to segregated network structures that reduce interactions between demographic groups and can amplify disparities
Group Fairness → contrastswith → Individual Fairness
confidence 92% · Most approaches aim to reduce disparities between demographic groups (group fairness). In contrast, a smaller number of methods focus on individual fairness
CrossWalk → isa → Random Walk-based Embedding
confidence 90% · CrossWalk [41] addresses this limitation by biasing walks toward nodes with more diverse neighborhoods
Statistical Parity → isa → Task-level Fairness Metric
confidence 90% · Common fairness metrics include statistical parity (SP) ... Task-level fairness evaluates whether the downstream predictions are fair
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Abstract
Abstract:Network embedding methods learn low-dimensional representations of graph-structured data to support downstream tasks such as node classification, link prediction, and influence maximization. However, real-world networks often reflect structural inequalities arising from demographic imbalances, homophily, and other societal biases, which fairness-agnostic embedding methods can encode and amplify. To address this issue, numerous fairness-aware network embedding methods have been proposed to mitigate bias while preserving embedding utility. This survey presents a comprehensive overview of fairness-aware network embeddings for complex networks. We propose a taxonomy that categorizes existing methods along three main complementary dimensions: underlying embedding approach (spectral, random walk, graph neural network, Bayesian, and method-agnostic), fairness intervention strategy (pre-processing, in-processing, and post-processing), and fairness objective criterion (embedding- or task-level). We further compare methods with respect to group versus individual fairness and assumptions regarding sensitive attributes. Finally, we discuss current limitations and highlight promising future research directions. This survey provides a unified perspective on fairness-aware network embedding and serves as a reference for developing fair and trustworthy network representation learning methods.
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- Source: https://arxiv.org/abs/2608.19381v1
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Fairness-Aware Network Embeddings: Methods, Applications, and Challenges Ella Has Affiliation: LIACS, Leiden University Leiden, The Netherlands e.has@liacs.leidenuniv.nl Harshith Kumar Yadav Affiliation: Dept. of Computer Science IIT Ropar, India e.23csz0002@iitrpr.ac.in Gaurav Dixit Affiliation: Mehta Family School of DS and AI IIT Roorkee, India gaurav.dixit@ms.iitr.ac.in Mykola Pechenizkiy Affiliation: Eindhoven University of Technology Eindhoven, The Netherlands m.pechenizkiy@tue.nl Akrati Saxena Affiliation: LIACS, Leiden University Leiden, The Netherlands a.saxena@liacs.leidenuniv.nl Abstract Network embedding methods learn low-dimensional representations of graph-structured data to support downstream tasks such as node classification, link prediction, and influence maximization. However, real-world networks often reflect structural inequalities arising from demographic imbalances, homophily, and other societal biases, which fairness-agnostic embedding methods can encode and amplify. To address this issue, numerous fairness-aware network embedding methods have been proposed to mitigate bias while preserving embedding utility. This survey presents a comprehensive overview of fairness-aware network embeddings for complex networks. We propose a taxonomy that categorizes existing methods along three main complementary dimensions: underlying embedding approach (spectral, random walk, graph neural network, Bayesian, and method-agnostic), fairness intervention strategy (pre-processing, in-processing, and post-processing), and fairness objective criterion (embedding- or task-level). We further compare methods with respect to group versus individual fairness and assumptions regarding sensitive attributes. Finally, we discuss current limitations and highlight promising future research directions. This survey provides a unified perspective on fairness-aware network embedding and serves as a reference for developing fair and trustworthy network representation learning methods. I Introduction Networks provide a fundamental abstraction for representing complex systems by modeling entities as nodes and their interactions as edges [74]. This representation naturally models a wide range of real-world systems, including social networks, citation networks, biological networks, transportation systems, financial transaction networks, and communication infrastructures. A central objective of network analysis is to extract meaningful information from the network structure to support downstream tasks such as node classification, link prediction, community detection, node ranking, influence maximization, anomaly detection, and graph classification. Network embedding has emerged as one of the most successful approaches to analyzing graph-structured data [15]. The goal of network embedding is to map each node to a low-dimensional vector space while preserving the network’s structural and attribute-based information (as shown in Fig. 1). These learned representations serve as features for developing machine-learning- and deep-learning-based models for downstream network analysis tasks. Classical embedding techniques include spectral methods [93], random-walk-based models such as DeepWalk [76] and Node2vec [25], and, more recently, graph neural networks (GNNs), such as GCN [43] and GraphSAGE [30], which have become the dominant paradigm for representation learning due to their expressive message-passing mechanism. Node embedding quality directly influences the performance of downstream network analysis tasks. Since embeddings are learned from network topology and node attributes, they can also inherit and amplify structural inequalities present in the underlying network, leading to bias in downstream task outcomes (Fig. 1). This may disadvantage minority groups through lower recommendation visibility [79], lower centrality rankings [92], reduced information access [86, 82], and poorer node classification performance [16, 19]. Real-world networks exhibit structural inequalities among individuals or groups, shaped by historical, societal, and behavioral processes that influence their evolution [81, 39, 69]. One important source of bias is group-size imbalance, in which minority groups are significantly underrepresented, thereby providing limited information for learning reliable representations [62]. Another major source is homophily [85], the tendency of individuals sharing similar characteristics, such as gender, ethnicity, age, or political affiliation, to connect more frequently with one another. Homophily leads to segregated network structures that reduce interactions between demographic groups and can amplify disparities in downstream predictions [55, 39]. Other evolution mechanisms, including preferential attachment [6], reciprocity, community formation, and core-periphery structure [83], further reinforce existing inequalities. As a result, network topology itself becomes a carrier of sensitive demographic information, leading to undue influence of sensitive attributes on task outcomes. For example, in attributed networks, sensitive attributes are often correlated with both network structure and node features, enabling downstream models to exploit protected attributes even when they are omitted from the input. Therefore, simply removing sensitive labels is insufficient to eliminate bias. These concerns have motivated the rapidly growing field of fairness-aware network embeddings, with the objective of learning representations that maintain predictive utility while reducing disparities across sensitive groups. In this survey, we present a comprehensive review of fairness-aware network embedding methods for complex networks. We introduce a taxonomy that categorizes existing approaches along three complementary dimensions: the underlying embedding approach, the fairness intervention strategy, and the fairness objective optimized. We further compare methods with respect to group versus individual fairness assumptions about sensitive attributes, and applicability to different network settings. Finally, we discuss the strengths and limitations of existing approaches, identify emerging research trends, and outline important open challenges to guide future research toward fair, scalable, and trustworthy embeddings. Fig. 1: An illustration of fairness-aware network embedding. (A) An example network with two demographic groups (orange and blue). (B) The corresponding adjacency matrix. (C) A sample low-dimensional embeddings. (D) A fairness-agnostic embedding (DeepWalk [76]) that preserves sensitive group information, potentially leading to biased downstream predictions. (E) A fairness-aware embedding (CrossWalk [41]) that mitigates the impact of sensitive attribute information, resulting in a fair outcome in downstream tasks. I Network Embeddings and Applications Let a graph be represented as G=(V,E,)G=(V,E,X), where V denotes the set of nodes, E⊆V×VE V× V is the set of edges, and X represents optional node attributes. The objective of network embedding is to learn a mapping f:V→ℝd,f:V ^d, that assigns each node v∈Vv∈ V a low-dimensional vector representation v=f(v)z_v=f(v), where d≪|V|d |V|. The embedding function is learned such that similar nodes in the original graph are mapped to nearby points in the embedding space. Depending on the embedding method, the optimization objective may preserve first-order proximity (direct connections), higher-order neighborhood relationships, structural similarity, community structure, or node attribute information. The learned embedding matrix ∈ℝ|V|×dZ ^|V|× d provides a compact representation of the graph that can be used as input features for a wide variety of downstream tasks, as explained below. Node Classification Given a set of labeled nodes ℒ⊆VL V, a classifier g:ℝd→g:R^d is trained on the corresponding node embeddings to predict labels for unlabeled nodes, where Y denotes the set of class labels [4]. Common choices include logistic regression [51, 50], label propagation [107, 41], support vector machines [32], multilayer perceptrons [73], and GNNs [30]. Link Prediction The objective of link prediction is to estimate whether an edge exists or is likely to form between two nodes. Given node embeddings, pairwise node features are constructed using operators such as concatenation, Hadamard product, L1 norm, L2 norm, or cosine similarity [25, 80]. These features are then used to train a machine learning model, often logistic regression, that predicts missing or future links. Node Ranking and Influence Maximization Node embeddings capture structural features that can be used to estimate node importance or centrality ranking [84]. A ranking function r(v)=h(v)r(v)=h(z_v) assigns an importance score to each node, where h(⋅)h(·) can be a learned regression model. For influence maximization, node embeddings can be clustered using k-medoids, and the top-k nodes from each cluster are selected with a group-aware seed selection strategy to maximize the spread of influence [41]. Anomaly Detection Network embeddings can also be used to identify anomalous nodes whose structural behavior differs substantially from the majority of the network [33]. Given the embedding matrix Z, anomaly scores can be computed using clustering, density estimation, nearest-neighbor distances, or reconstruction errors. Nodes with isolated embeddings or high reconstruction errors are identified as potential anomalies. Network embeddings have also been widely applied to community detection [91], recommendation systems [108], graph classification [68], graph matching [57], visualization [5], and network alignment [13]. By providing a low-dimensional representation that captures both local and global structural information, embeddings enable conventional machine learning models to operate effectively on graph-structured data. I Taxonomy In this survey, we classify fair network embedding methods along three dimensions: underlying embedding approach, fairness intervention strategy, and fairness objective. Additionally, we discuss group and individual fairness and requirements on the sensitive attributes. I-A Embedding Approach Fair network embedding methods can be classified by their underlying embedding approach: spectral embedding, random walk-based embedding, GNNs, Bayesian modeling, and method-agnostic approaches, with GNNs constituting the vast majority. Method-agnostic approaches propose bias-mitigating strategies that can be applied regardless of the training approach. For example, some methods reduce bias by augmenting the input graph [55], which can then be embedded by any method. I-B Fairness Intervention Strategy The second dimension classifies methods according to how and when fairness is introduced into the embedding pipeline, i.e., pre-processing, in-processing, post-processing, and hybrid frameworks [54, 105]. I-B1 Pre-processing methods modify the input graph before learning node embeddings. Their objective is to reduce structural sources of bias, for example, by adding or removing edges to reduce homophily [14, 90] or rebalance connectivity between demographic groups [55]. I-B2 In-processing methods incorporate fairness directly into the embedding process. Existing approaches achieve this through three main mechanisms: graph augmentation, rebalancing, and objective function modification. Graph augmentation dynamically perturbs the graph during training, generating different graph views to encourage fair representations [1]. Rebalancing techniques adjust the learning process by modifying sampling probabilities [9], random walk transitions [79, 41], or GNN message passing [118, 59] and attention [48, 66] weights to ensure a more balanced representation of different groups. Fairness can be incorporated into the objective function through: a) Constraints: restricting the search space [44]; b) Regularization: penalizing bias metrics [50, 2]; c) Adversarial learning: obscuring sensitive attributes from an adversarial discriminator [7, 16]; d) Contrastive learning: aligning embeddings across fairness-aware graph views [49]; e) Disentanglement: separating task-relevant and sensitive information [28, 120]. I-B3 Post-processing methods improve fairness after training. They either transform the learned embeddings (e.g., by decorrelating them from sensitive attributes [75]) or adjust the outputs of downstream tasks to produce fair decisions without retraining the model [54, 23]. I-C Fairness Objective The third dimension of our taxonomy categorizes methods according to the fairness objective they optimize. Existing methods generally target fairness at either (i) the embedding level or (i) the downstream task level. I-C1 Embedding-level fairness considers to what extent embeddings encode sensitive attributes. This is typically evaluated with the correlation between node embeddings and sensitive attributes or the Representation Bias (RB), which quantifies the ability of a classifier to predict sensitive attributes from the embeddings. Lower correlation or prediction accuracy indicates that the embeddings encode less sensitive information. I-C2 Task-level fairness evaluates whether the downstream predictions are fair across demographic groups. Common fairness metrics include statistical parity (SP), equality of opportunity (EO), and performance disparity across groups. SP requires favorable outcomes to be independent of sensitive attributes, while EO requires equal true positive rates across groups. Performance disparity measures differences in predictive performance across demographic groups, for example, using variance. Additionally, several methods optimize task-specific fairness objectives that may not generalize to fairness in other tasks, such as balanced cluster composition [44, 29] or increased inter-group link prediction [79, 80]. I-D Additional Methodological Characteristics Beyond the three primary dimensions of our taxonomy, fairness-aware network embedding methods also differ in several methodological characteristics, as discussed below. I-D1 Group vs. individual fairness Most approaches aim to reduce disparities between demographic groups (group fairness). In contrast, a smaller number of methods focus on individual fairness [29, 20], ensuring that structurally or semantically similar nodes receive similar outcomes. I-D2 Binary vs. multi-class sensitive attributes Many existing methods assume a single binary sensitive attribute for simplicity. However, some approaches naturally support multi-class sensitive attributes [72] or can be extended to settings involving more than two demographic groups. I-D3 Single vs. multiple sensitive attributes While most methods consider only one sensitive attribute, some address multiple or intersectional attributes (e.g., gender and ethnicity simultaneously), enabling fairness across overlapping demographic groups [8, 105]. I-D4 Availability of sensitive attributes Most fairness-aware embedding methods assume that sensitive attributes are available for all nodes during training. More recent approaches relax this assumption by handling partially observed sensitive attributes [16, 26] or eliminating the need for them altogether through feature-blind learning [100]. The upcoming sections (IV-VIII) cover fair embedding methods categorized by their underlying approach. IV Spectral Embedding Spectral embedding methods learn node representations by performing eigenvalue decomposition on the network’s Laplacian matrix and using the eigenvectors corresponding to its smallest eigenvalues as embeddings [93]. Fairness-aware spectral embedding methods primarily improve fairness through fairness constraints or regularization. IV-A Fairness Constraints Fairness constraints in spectral embedding encourage balanced node representations across sensitive groups. Kleindessner et al. [44] formulated fair spectral clustering by constraining the optimization so that each cluster reflects the demographic composition of the network. This is achieved by transforming the graph Laplacian using the proportional group sizes before eigenvalue decomposition. Wang et al. [94] later improved the scalability of this approach. Beyond group fairness, Gupta and Dukkipati [29] extended spectral clustering to individual fairness by constraining nodes to receive similar representation in each cluster. FNM [54] further combines fairness-constrained spectral embedding with balanced k-means clustering, enforcing demographic balance throughout the clustering process. IV-B Fairness Regularization DFaR [50] adopts a regularization approach that penalizes the correlation between node embeddings and sensitive attributes. It first learns node and feature embeddings using unconstrained spectral embedding, and then applies a correlation penalty to learn the optimal merging of node and feature embeddings. DFaR can also be used for dynamic networks. V Random Walk-based Embedding Random walk-based embedding methods, also known as skip-gram embedding, such as DeepWalk [76] and Node2vec [25], generate random walks to capture the context of each node and learn embeddings using the skip-gram model [71], which distinguishes context nodes from randomly sampled negative nodes. Fairness-aware variants primarily mitigate bias by modifying either the random-walk sampling process or the negative-sampling strategy. V-A Rebalancing Most fairness-aware random walk methods improve fairness by rebalancing random walk sampling to collect an equitable context for each node. Fairwalk [79] balances random walk transition probabilities across all groups, ensuring equal group representation in sampled walks. However, Fairwalk does not account for the possibility that nodes might have neighbors only of the same group, causing walks to remain stuck within one group and over-represent it. CrossWalk [41] addresses this limitation by biasing walks toward nodes with more diverse neighborhoods near group boundaries, while MoonWalk [72] extends this idea to multi-group settings. NodeSim [80] introduces a similarity-aware random walk based on node similarity and community structure to better capture inter-community relationships, with fairness evaluated through inter- and intra-community link prediction. V-B Negative Sampling Unlike sampling-based approaches, residual2vec [45] mitigates bias by modifying the negative sampling distribution. It generates randomized graphs that preserve only bias-inducing properties, such as node degree and inter-/intra-group connectivity, and draws negative samples according to node-pair frequencies in these graphs, filtering out the effect of sensitive-attribute homophily on random walks by sampling nodes from the same group more often as negative pairs while providing a flexible framework that could model any bias-inducing properties in the randomized graphs. VI Graph Neural Networks Graph neural networks (GNNs) are deep learning models specifically designed for graph-structured data that learn embeddings by jointly exploiting node features and graph topology [43, 30]. At each layer, a node aggregates its neighbors’ features, known as message passing. The parameters of the aggregation function are trained for optimal embedding utility. After multiple layers, the node embeddings capture both local neighborhood information and higher-order structural patterns, making them highly effective for downstream tasks. VI-A Rebalanced Message Passing Fair message passing is an in-processing approach that mitigates bias during neighborhood aggregation, where graph structure can propagate and amplify sensitive information. VI-A1 Fair Message Aggregation Fair message aggregation approaches rebalance the contribution of each sensitive group, either by sampling an equal number of neighbors per group [59] or by reweighting each group’s contribution. FairAGG [118] uses Shapley values to estimate the fairness contributions of intra- and inter-group edges and reweights their messages accordingly. FAME [77] offers a lightweight solution that directly modifies each GCN message or GAT attention logit in A-FAME according to the difference in sensitive attributes between connected nodes. DegFairGNN [63] improves degree fairness by learning contexts that enrich information for low-degree nodes and distill information for high-degree nodes. Fair Graph U-net [99] introduces fairness into hierarchical representation learning by balancing group representation during pooling, while distributing the cost of group fairness more evenly across individuals. Im-GBK [58] handles homophilic and heterophilic neighbors separately. HetroFair [24] reduces popularity bias in a recommendation system by inversely weighting user–item messages based on their similarity, suppressing popular items and strengthening long-tail contributions. IntFair [27] promotes consistent recommendation performance across categories preferred by users through TOPSIS-based [35] balanced neighbor sampling. VI-A2 Fair Attention Weights FairGAT [48] allocates theoretically determined attention budget for inter-group neighbors. FairGT [66] extends this by constructing sensitive-aware multi-hop token sequences and combines them with selected adjacency eigenvectors before Transformer attention. VI-B Fairness Regularization Another common in-processing approach in fair GNNs is fairness regularization, which adds some measurement of bias as a penalty to the loss function. Unfairness is penalized by measuring bias at the embedding or at the outcome level. VI-B1 Embedding-Level Penalties DFGNN [73] proposes two ways to measure unfairness as the distance between embedding distributions between groups: comparing a summary metric by taking the difference in means, later also used by FairNorm [47], or comparing the shape of the distributions with Wasserstein distance [38]. FairGAE [22] pairs Wasserstein distance penalization with balanced message passing. FairHGNN [9] uses it in a GNN for Heterogeneous Information Networks by sampling meta-paths with balanced probabilities for each group. FAHIN [11] additionally adaptively changes the importance of the fairness regularization term. Others have suggested different metrics. GMMD [116] uses the summary metric Maximum Mean Discrepancy (MMD) [3]. FairGLite [104] learns a mask that hides sensitive attributes with one penalty term penalizing the distance between embedding distributions of groups, and another penalizing correlation with sensitive labels. Missing labels are first estimated, and nodes with more certain labels are more heavily regularized. EAGNN [113] compares fairness at both the embedding and the task level with regularization terms minimizing embedding distance between similar nodes from different groups and maximizing statistical parity. In contrast, the feature-blind method Fairwos [95] penalizes misalignment between embeddings of similar nodes by extracting pseudo-sensitive attributes from graph structure and node features. VI-B2 Task-Level Penalties On the other hand, FMP [36] penalizes disparities at the task outcome level using statistical parity (SP), while FS-GNN [115] penalizes the difference in utility loss between groups. Agrawal et al. [2] applied equality of opportunity (EO) as their measure of fairness in a federated learning setting where embeddings are updated locally to preserve privacy, while EO is estimated in a privacy-preserving way by aggregating noisy performance and group membership data across users. REDRESS [20] ensures individual fairness by penalizing the distance between the ranking of nodes with the most similar characteristics and the ranking of nodes with the most similar outcomes. ComFairGNN [88] debiases by encouraging nodes with the same class label across groups and local structures to receive comparable embeddings regardless of sensitive attributes. In the case of unavailable sensitive labels, FairINV [117] identifies group partitions where the GNN exhibits performance disparities and penalizes loss variation across these sensitive group partitions. VI-C Adversarial Learning Adversarial fair GNNs learn node embeddings that remain informative for downstream tasks while preventing sensitive attribute leakage by obscuring the sensitive information from an adversarial model attempting to decode it. Bose et al. [7] adversarially trained attribute-specific MLP filters to remove sensitive attributes from embeddings. Similarly, Khajehnejad et al. [42] used an adversarial autoencoder. FairVGNN [96] addresses sensitive attribute leakage by adversarially learning multiple masked feature views and adaptively weight-clamping to limit sensitive-related feature channels. FairGNN [16] extends adversarial learning to graphs with limited available sensitive labels by estimating missing sensitive attributes and combining adversarial debiasing with covariance regularization, while FairAC [26] combines attention-based attribute completion with adversarial learning. NT-FairGNN [17] extends FairGNN by privatizing sensitive attributes and estimates them using a noise-corrected loss. FairHELP [10] adapts adversarial learning for Heterogeneous Information Networks by making the adversary predict the sensitive attributes involved in the edges. FPGNN [110] combines adversarial representation learning with a novel Fair Path pruning strategy to mitigate sensitive information leakage from high-degree nodes that are identified through fair random walks. MVFGNN [111] combines original, diffusion and feature-similarity graph views through a variational graph autoencoder (VGAE) and similarity-based weighting before adversarially removing sensitive information. VI-D Contrastive Learning Fair GNNs based on contrastive learning learn bias-resistant node embeddings by aligning representations across fairness-aware graph views while separating unrelated nodes. Kose et al. [49] created graph views with edge deletion and feature masking to reduce biased connectivity patterns. FairMigration [34] pretrains a GNN on counterfactual views with flipped sensitive attributes and adversarially removes residual sensitive information from these migrated groups. FairMIB [61] addresses multiple sources of bias by separating the graph into a feature, structural, and diffusion view. Independent variational encoders learn these views, which are then aligned with cross-view contrastive learning. FairDGE [56] maintains degree fairness in dynamic graphs, where node degrees change over time, using contrastive learning and group-wise utility loss alignment. FairGCL [18] applies the contrastive learning framework to influence maximization using a Principal Neighbourhood Aggregation (PNA) encoder and a task-specific loss. VI-E Disentanglement Disentanglement-based GNNs separate task-relevant information from sensitive information within node representations. CAF [28] does so by selecting counterfactual proxy nodes with comparable content but distinct sensitive environments to estimate which components of the embeddings relate to sensitive attributes. SCCAF [40] extends CAF to enhance the discriminative quality of disentangled embeddings. FDGNN [98] considers sensitive information from both node attributes and neighborhoods by finding counterfactual ego graphs in the network to disentangle sensitive and non-sensitive latent factors. Instead of counterfactual samples, FairSAD [120] learns masks to decorrelate independent latent features and sensitive attributes. FairGID [12] also masks sensitive attributes in the features and then learns a structural representation separately. The two representations are then combined with adversarial learning, further reducing sensitive attribute leakage. Similarly, DAB-GNN [52] disentangles attribute, structural, and attribute-structure interaction biases independently, while Wasserstein distance is used to align embedding distributions across groups. FairMI [114] disentangles embeddings by training a discriminator with the sensitive component and minimizing mutual information with the sensitive-free component. FGLISA [103] addresses unknown sensitive attributes with a causal variational graph encoder that separates sensitive-related and sensitive-unrelated representations, infers soft sensitive labels, and aligns group distributions. FairGNN-WOD [101] needs no sensitive attribute labels at all with a VAE that infers sensitive attribute proxies, while Themis [100] estimates reliable proxies with a causal Bayesian VAE that separates sensitive and task-related information. VI-F Graph Augmentation Graph augmentation in GNNs can be used as a pre- or in-processing step to reduce bias in the input graph or to gain robustness against perturbation of sensitive attributes. VI-F1 Reduced Bias in Input Graph Several approaches propose GNN pipelines that perturb the input graph to reduce bias. EDITS [21] perturbs both the adjacency matrix and the node features to minimize the distance between the feature distributions of two sensitive groups and the distance between feature distributions after rounds of message-passing. G-FAME [64] pre-processes the graph with edge deletion to reduce homophily and addresses the loss of information inherent in removing edges from the graph with a mixture of experts more capable of learning from this limited information. FairSample [14] connects nearby nodes with similar features and the same (known or estimated) class label but different sensitive attributes and then performs balanced message-passing learned with reinforcement learning. Geb[97] uses evolutionary search to find unfair subgraphs in a trained GNN. It modifies edges and node features to reduce group differences and updates only the impacted nodes. VI-F2 Improved Robustness Another use of graph augmentation is improving robustness against perturbation of the sensitive attributes. Nifty [1] generates two alternative graphs at each training step, one with augmented edges and node features for learning stability and one with augmented sensitive attributes for fairness. A GNN is trained to achieve similarity between the embeddings of the original and the two augmented graphs. Similarly, AdaLipGNN [87] achieves fairness as a byproduct of robustness to graph and feature perturbations. FairCNCB [106] generates realistic counterfactual nodes by changing sensitive attributes while preserving labels and graph structure. It prioritizes minority groups during training and ensures consistent predictions for original and generated nodes. Ma et al. [67] also included the influence of the neighbors’ sensitive attributes on a node’s embeddings with a causal model that generates counterfactual ego graphs in which either the sensitive attributes of neighbors or of the central node are changed, and the node features are altered accordingly. VI-G Hybrid Methods Hybrid approaches combine the methods discussed above. RFCGNN+ [102] combines multi-frequency message passing to reduce topology bias and counterfactual nodes to disentangle sensitive information, while reducing differences between sensitive groups. FDGNN [112] uses counterfactual augmentation and disentangled contrastive learning to separate task-relevant representations from sensitive components. MAPPING [89] debiases both node features and graph topology before training with fairness regularization, adversarial feature reconstruction, fair message passing, and edge pruning. SRGNN[109] augments the graph by strengthening low-degree nodes and reducing high-degree connections and uses an adversarial discriminator to remove sensitive information from embeddings. VI-H Other Methods The following methods propose unique strategies that do not fit into the categories above. FairDTD [53] reduces feature and topology bias by transferring fairness knowledge from MLP and GCN teacher models trained on partial data into a student GNN. FairGKD [119] combines the knowledge of both teachers into a single synthetic teacher. FairGE [65] pre-processes the data by zero-padding missing sensitive attributes and filtering out sensitive information with spectral truncation of structural encoding as input to a Graph Transformer. VII Bayesian Modeling Conditional Network Embedding [37] learns node embeddings using Bayes’ rule. DeBayes [8] introduces a fair prior that encodes both structural properties (e.g., degree) and sensitive attributes so the likelihood does not need to represent the sensitive attributes for a good fit with the network. The learned likelihood and a prior with only structural properties define the embeddings, filtering out all sensitive information. VIII Method-Agnostic Approaches Unlike approaches that modify a specific embedding method, method-agnostic approaches introduce fairness strategies with no requirements on the model’s architecture. VIII-A Graph Augmentation A common method-agnostic bias mitigation strategy is to alter the input graph so that the effects of sensitive attributes on the graph structure are reduced. FairLP [55] pre-processes the input graph by adding and removing edges to achieve equal density in each group because this is an important factor in link prediction accuracy disparity. FairDrop [90] takes an in-processing approach, removing edges between nodes in the same group from the original graph at each training step to reduce homophily. This can be applied to any embedding backbone that learns in multiple iterations, including random-walk methods and GNNs. Instead of augmenting graphs using heuristics such as reducing homophily, Ling et al. [60] trained a GNN model, Graphair, with adversarial learning to produce augmented graphs that hide sensitive attributes while keeping similar network structure, node features, and final embeddings. VIII-B Filtering Sensitive Attributes Another approach is to filter out sensitive information from the embeddings. MONET [75] is an in-processing approach that orthogonalizes the embeddings of sensitive attributes and topological embeddings with eigenvalue decomposition at every training step. On the other hand, Kose et al. [46] designed a graph filter approach that can be applied as a pre- or post-processing step. A graph signal (e.g., input node attributes or output embeddings or labels) is transformed into the frequency domain to filter out part of the signal that corresponds to the sensitive attributes. The post-processing approach FairGo [105] learns a filter for each dimension of the sensitive attributes with adversarial learning to obscure sensitive information. VIII-C Fairness Regularization FairMILE [31] uses a combination of pre- and post-processing by first merging strongly connected nodes with different sensitive attributes into diverse supernodes and then learning embeddings on the coarsened graph. The coarse embeddings are refined to obtain embeddings for each node in the original graph with an objective function that penalizes the distance between embeddings in different groups. VIII-D Task-Level Debiasing Fairness constraints can also be enforced at the task level. FSGNN [23] applies this idea to influence maximization by selecting nodes from each group proportionally to the estimated total influence of that group. IX Emerging Trends and Future Directions In this section, we discuss emerging trends and suggestions for future research. IX-A Sensitive Attributes: Missingness and Intersectionality Existing methods largely rely on sensitive attributes during training, which are often unavailable due to privacy or data limitations. Developing feature-blind methods that detect and mitigate structural bias remains a key challenge. Methods that address (partial) missing sensitive attributes usually do so by predicting them before applying fairness constraints [16, 101]. However, inaccurate predictions may introduce additional bias, particularly when missingness is not random and disproportionately affects minority groups. Future methods should explicitly model uncertainty and missingness mechanisms rather than relying solely on imputed sensitive labels. Additionally, most existing methods consider a single binary sensitive attribute, whereas real-world applications involve multiple interacting demographic characteristics. Extending fairness objectives to intersectional and multi-class settings remains a significant challenge [70, 8, 105]. IX-B Understanding Bias Many existing approaches mitigate bias without explicitly modeling how it arises within the network [16, 73]. Conversely, graph augmentation and rebalancing methods often rely on assumptions regarding homophily, structural imbalance, or preferential attachment [55, 90]. Understanding whether fairness interventions should explicitly model bias-generating mechanisms or remain agnostic to them is an important theoretical question that deserves further investigation. Additionally, developing interpretable methods that explain fair decisions will offer insights into the impact of structural biases and the effects of fairness interventions, and help design fair explainable methods. Relatedly, a better understanding of the fairness-utility trade-off remains a key challenge. Developing principled optimization methods and theoretical guarantees for navigating this trade-off rather than relying on hyperparameter optimization will benefit the field. IX-C Novel Strategies for Fair Random Walk-based Embeddings Existing fair random walk-based methods modify transition probabilities or sampling strategies. Extending techniques such as fairness regularization and adversarial learning, which have proven effective in GNNs, represents a promising direction for improving fairness in random walk-based embeddings. IX-D Scalability, Higher-order Networks and Generalization Existing methods usually scale poorly to large networks and are only applicable to static homogeneous networks with pairwise interactions. Additional optimization objectives and fairness constraints often limit scalability. Developing scalable fair algorithms while maintaining computational efficiency remains an important research direction [47, 94]. Additionally, real-world networks evolve over time, yet fair embedding methods that efficiently adapt to dynamic networks remain relatively underexplored [50, 56]. Moreover, extending embedding methods to heterogeneous networks with multiple node and edge types [10, 9] as well as hypergraphs and other higher-order network structures, remains largely unexplored. Furthermore, most existing GNNs and spectral methods optimize fairness for a specific downstream task, limiting their generalizability. Developing fair embeddings that preserve fairness across diverse downstream network analysis tasks would improve practical applicability. IX-E Benchmark Datasets and Standardized Evaluation Existing methods are evaluated on different datasets, tasks, and fairness metrics, hindering meaningful comparisons. The community would benefit from standardized benchmark datasets, evaluation protocols, and reproducible experimental settings specifically designed for fair embeddings [78]. X Conclusion Network embeddings have become a fundamental building block for analyzing graph-structured data and performing downstream network analysis tasks, making fairness an increasingly important consideration in their development. 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