A subgraph-based ranking system for professional tennis players

Abstract

This paper introduces a novel ranking system for competitive sports based around the notion of subgraphs. Although the system is targeted specifically to professional tennis it could be applied to any dominance network due to its generality. The results of about 140,000 tennis matches played between Top-100 players are used to create a colored directed network where colors represent different surfaces and edge direction depends on head-to-read results between players. The main contribution of this work is a ranking system which relies on the occurrences of 4-node directed subgraphs and the positions (or orbits) where the players appear on them. Since the concept of orbit is intrinsically connected with node dominance, appearing frequently in dominant orbits indicates that the player himself is dominant. Even in a very sparse network and without any background knowledge on the tournaments or stages of the matches, our proposal is able to extract meaningful rankings which capture the intricate competitive relationships between players from different eras.