Self-organization of social hierarchy on interaction networks

Abstract

In order to examine the effects of interaction network structures on the self-organization ofsocial hierarchy, we introduce the agent-based model: each individual as on a nodeof a network has its own power and its internal state changes by fighting withits neighbors and relaxation. We adopt three different networks: regular lattice,small-world network and scale-free network. For the regular lattice, we find theemergence of classes distinguished by the internal state. The transition points whereeach class emerges are determined analytically, and we show that each class ischaracterized by the local ranking relative to their neighbors. We also find that theantiferromagnetic-like configuration emerges just above the critical point. For theheterogeneous networks, individuals become winners (or losers) in descending order of thenumber of their links. By using mean-field analysis, we reveal that the transitionpoint is determined by the maximum degree and the degree distribution in itsneighbors.