title: Bayesian inference of natural rankings in incomplete competition networks.
abstract: Competition between a complex system's constituents and a corresponding reward mechanism based on it have profound influence on the functioning, stability, and evolution of the system. But determining the dominance hierarchy or ranking among the constituent parts from the strongest to the weakest--essential in determining reward and penalty--is frequently an ambiguous task due to the incomplete (partially filled) nature of competition networks. Here we introduce the "Natural Ranking," an unambiguous ranking method applicable to a round robin tournament, and formulate an analytical model based on the Bayesian formula for inferring the expected mean and error of the natural ranking of nodes from an incomplete network. We investigate its potential and uses in resolving important issues of ranking by applying it to real-world competition networks.
authors.affiliation: Graduate School of Culture Technology, Korea Advanced Institute of Science and Technology, Daejeon, Republic of Korea 305-701 and Physics Department, Kyung Hee University, Seoul, Republic of Korea 130-701.
authors.forename: Juyong
authors.initials: J
authors.lastname: Park
authors.affiliation: Physics Department, Kyung Hee University, Seoul, Republic of Korea 130-701.
authors.forename: Soon-Hyung
authors.initials: SH
authors.lastname: Yook