Inherent Limits on Topology-Based Link Prediction

TL;DR

This paper establishes fundamental upper bounds on the effectiveness of topology-based link prediction, revealing inherent limitations especially in sparse graphs and emphasizing the need for additional information.

Contribution

It introduces theoretical bounds on link prediction accuracy based solely on graph topology, highlighting limitations in sparse real-world graphs.

Findings

Upper bounds on link prediction accuracy are low in sparse graphs.

Graph automorphisms impose fundamental limits on predictability.

Topology alone is insufficient for high-accuracy link prediction in many cases.

Abstract

Link prediction systems (e.g. recommender systems) typically use graph topology as one of their main sources of information. However, automorphisms and related properties of graphs beget inherent limits in predictability. We calculate hard upper bounds on how well graph topology alone enables link prediction for a wide variety of real-world graphs. We find that in the sparsest of these graphs the upper bounds are surprisingly low, thereby demonstrating that prediction systems on sparse graph data are inherently limited and require information in addition to the graph topology.