A generalized theory of preferential linking

TL;DR

This paper investigates how different preferential linking mechanisms influence social network evolution, proposing a generalized model that explains diverse network features and their underlying growth processes.

Contribution

It introduces a unified analytical framework for preferential linking, validating linear preference empirically, and revealing how simple rules lead to complex network structures.

Findings

Empirically validated linear preference in social networks

Derived analytical degree distributions for 27 preference scenarios

Identified complex network structures emerging from simple sublinear preferences

Abstract

There are diverse mechanisms driving the evolution of social networks. A key open question dealing with understanding their evolution is: How 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, present unified analytical results describing network characteristics for 27 preference scenarios, and explore the relation between preferential linking mechanism and network features. We 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.