k-hop Fairness: Addressing Disparities in Graph Link Prediction Beyond First-Order Neighborhoods

TL;DR

This work proposes $k-hop fairness, a structural notion of fairness for LP that assesses disparities conditioned on the distance between nodes in the graph, and formalizes this notion through predictive fairness and structural bias metrics, and proposes pre- and post-processing mitigation strategies.

Abstract

Link prediction (LP) plays a central role in graph-based applications, particularly in social recommendation. However, real-world graphs often reflect structural biases, most notably homophily, the tendency of nodes with similar attributes to connect. While this property can improve predictive performance, it also risks reinforcing existing social disparities. In response, fairness-aware LP methods have emerged, often seeking to mitigate these effects by promoting inter-group connections, that is, links between nodes with differing sensitive attributes (e.g., gender), following the principle of dyadic fairness. However, dyadic fairness overlooks potential disparities within the sensitive groups themselves. To overcome this issue, we propose $k$-hop fairness, a structural notion of fairness for LP, that assesses disparities conditioned on the distance between nodes in the graph. We formalize this notion through predictive fairness and structural bias metrics, and propose pre- and post-processing mitigation strategies. Experiments across standard LP benchmarks reveal: (1) a strong tendency of models to reproduce structural biases at different $k$-hops; (2) interdependence between structural biases at different hops when rewiring graphs; and (3) that our post-processing method achieves favorable $k$-hop performance-fairness trade-offs compared to existing fair LP baselines.

Figures (21)

• Figure 1: In this example, nodes A and B are segregated within a cluster of blue nodes. While a dyadic view would produce likely inter-edges (typically between nodes with shared neighbors around node C), $k$-hop fairness allows specifying the order at which fairness is desired (here, $k=3$), enabling connections to the segregated part.
• Figure 2: Comparison between graph structural bias and classical LP models $k$-hop fairness across meaningful hops.
• Figure 3: Influence of $NB^{(k)}$ minimization via edge addition on structural bias at other hops. All p-values reported were found to be below 0.01, indicating statistical significance. The evolution of biases over iterations is shown in Supplementary E.2. For some target $k$, the optimization process did not identify edges that reduce bias, these cases were excluded from the analysis.
• Figure 4: AUC vs $NF^{(k)}$ plot for base and fairness-aware GNN-based baselines and for targeted $k$ values. Our post-processing results are shown through arrows from base models. The star marker denotes the hypothetical model achieving the best AUC and the best $NF^{(k)}$ across baselines. Only baselines with AUC $> 0.55$ are displayed. The outcome of our post-processing approach on the base models are represented with an arrow. Figure (d) shows $\alpha$ effect in the post-processing method for SAGE predictions.
• Figure 5: Sensitive star graph with $n=12$ and $p=\frac{2}{3}$

Theorems & Definitions (12)

• Definition 1
• Definition 2: $k$-hop node attribute exposure
• Definition 3: $k$-hop group exposure
• Definition 4: $k$-hop neighborhood fairness
• Definition 5
• proof
• Definition 6
• proof
• Corollary 1
• proof