On the skewed degree distribution of hierarchical networks

Abstract

In this paper, a prestige-based evolution process is introduced, which provides a formal framework for the study of linear hierarchies seen in human societies. Due to the deterministic characteristics of the proposed model, we are capable of determining equilibria in closed form. Surprisingly, these stationary points recover the power-law degree distribution as the shared property of the resulting hierarchal networks, explaining the prevalence of hierarchies in societies. This result sheds light on the evolutionary advantages of hierarchies.