title: Ranking competitors using degree-neutralized random walks.
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.
authors.affiliation: Graduate School of Culture Technology, Korea Advanced Institute of Science & Technology, Daejeon, Republic of Korea.
authors.forename: Seungkyu
authors.initials: S
authors.lastname: Shin
authors.affiliation: Theory of Condensed Matter, Cavendish Laboratory, CB3 0HE, Cambridge, The United Kingdom.
authors.forename: Sebastian E
authors.initials: SE
authors.lastname: Ahnert
authors.affiliation: Graduate School of Culture Technology, Korea Advanced Institute of Science & Technology, Daejeon, Republic of Korea.
authors.forename: Juyong
authors.initials: J
authors.lastname: Park
mesh_terms: D000465:Algorithms; D005075:Biological Evolution; D003198:Computer Simulation; D013269:Stochastic Processes