FairGE: Fairness-Aware Graph Encoding in Incomplete Social Networks

TL;DR

FairGE tackles fairness in Graph Transformers over incomplete social networks by avoiding sensitive-attribute reconstruction and instead encoding fairness through the $m$ largest eigenvectors of the adjacency matrix, complemented by zero-padding for missing attributes. Theoretical results show that non-principal spectral components are suppressed, enabling multi-hop information to be captured while preserving independence from incomplete attributes. Empirically, FairGE achieves at least a 16% improvement in both statistical parity and equality of opportunity across seven real-world datasets, with competitive accuracy and reduced privacy risks due to non-reconstruction of sensitive data. This approach provides a practical, privacy-preserving pathway to fair GTs in real-world scenarios with incomplete sensitive information.

Abstract

Graph Transformers (GTs) are increasingly applied to social network analysis, yet their deployment is often constrained by fairness concerns. This issue is particularly critical in incomplete social networks, where sensitive attributes are frequently missing due to privacy and ethical restrictions. Existing solutions commonly generate these incomplete attributes, which may introduce additional biases and further compromise user privacy. To address this challenge, FairGE (Fair Graph Encoding) is introduced as a fairness-aware framework for GTs in incomplete social networks. Instead of generating sensitive attributes, FairGE encodes fairness directly through spectral graph theory. By leveraging the principal eigenvector to represent structural information and padding incomplete sensitive attributes with zeros to maintain independence, FairGE ensures fairness without data reconstruction. Theoretical analysis demonstrates that the method suppresses the influence of non-principal spectral components, thereby enhancing fairness. Extensive experiments on seven real-world social network datasets confirm that FairGE achieves at least a 16% improvement in both statistical parity and equality of opportunity compared with state-of-the-art baselines. The source code is shown in https://github.com/LuoRenqiang/FairGE.

Figures (4)

• Figure 1: Impact of different missing rates of sensitive attributes on fairness-aware methods (FMP jiang2024chasing, FairGT luo2024fairgt, and FairSIN yang2024fairsin) on the Credit dataset yeh2009the. $\Delta_{\text{SP}}$ is reported as the fairness metric (see Section \ref{['Metrics']}), where higher values indicate lower fairness. Lighter bars correspond to results on complete data, while darker bars indicate the additional increase due to missing attributes. For instance, in FMP, $\Delta_{\text{SP}}$ is about 0.78 with complete data but increases to around 1.6 at a missing rate of 0.1.
• Figure 2: The illustration of FairGE. For graphs containing two sensitive attributes (represented as red and blue) alongside incomplete sensitive attributes (white), FairGE effectively restores and preserves the original sensitive attributes while also capturing multi-hop neighbour information.
• Figure 3: Comparison of $\Delta_{\text{SP}}$ between FairGE and baseline models.
• Figure 4: Comparison of $\Delta_{\text{EO}}$ between FairGE and baseline models.