A generalized theory of preferential linking

Abstract

There are diverse mechanisms driving the evolution of social networks. A key open question dealing with understanding their evolution is: How do various preferential linking mechanisms produce networks with different features? In this paper we first empirically study preferential linking phenomena in an evolving online social network, find and validate the linear preference. We propose an analyzable model which captures the real growth process of the network and reveals the underlying mechanism dominating its evolution. Furthermore based on preferential linking we propose a generalized model reproducing the evolution of online social networks, and present unified analytical results describing network characteristics for 27 preference scenarios. We study the mathematical structure of degree distributions and find that within the framework of preferential linking analytical degree distributions can only be the combinations of finite kinds of functions which are related to rational, logarithmic and inverse tangent functions, and extremely complex network structure will emerge even for very simple sublinear preferential linking. This work not only provides a verifiable origin for the emergence of various network characteristics in social networks, but bridges the micro individuals’ behaviors and the global organization of social networks.