A Theoretical Perspective on Link Prediction Heuristics

Abstract

In network analysis, nodes with different degrees are usually weighted differently in tasks such as link prediction. For example, two individuals connected to the same high-degree node (e.g., a celebrity) are often considered less likely to know each other than if they share a low-degree connection. In this paper, we theoretically justify the reasoning behind this heuristic using a graph generation model. In this model, nodes are embedded in a latent metric space, and edges are more likely to form between nearby nodes. We analytically derive degree-based weighting schemes for commonly used link prediction and similarity measures. In particular, we identify the optimal weighting scheme for the Common Neighbors index and extend our analysis to other popular heuristics, including the graph distance. Our theoretical findings align with previous empirical observations, and we further validate them through experiments on both synthetic and real-world networks.