Ranking Competitors Using Degree-Neutralized Random Walks

TL;DR

This paper introduces a degree-neutralized random walk method for ranking competitors in complex networks, effectively reducing degree bias and improving accuracy over existing methods in real-world competition networks.

Contribution

The paper presents a novel ranking approach using degree-neutralized random walks that accounts for network structure and outperforms traditional methods in sparse networks.

Findings

Outperforms baseline win-loss methods in sparse networks

Reduces degree-induced bias in rankings

Provides stable and accurate rankings in real-world data

Abstract

Competition is ubiquitous in many complex biological, social, and technological systems, playing an integral role in the evolutionary dynamics of the systems. It is often useful to determine the dominance hierarchy or the rankings of the components of the system that compete for survival and success based on the outcomes of the competitions between them. Here we propose a ranking method based on the random walk on the network representing the competitors as nodes and competitions as directed edges with asymmetric weights. We use the edge weights and node degrees to define the gradient on each edge that guides the random walker towards the weaker (or the stronger) node, which enables us to interpret the steady-state occupancy as the measure of the node's weakness (or strength) that is free of unwarranted degree-induced bias. We apply our method to two real-world competition networks and explore the issues of ranking stabilization and prediction accuracy, finding that our method outperforms other methods including the baseline win--loss differential method in sparse networks.