Consecutive partitions of social networks between rivaling leaders

TL;DR

This paper introduces a model algorithm to analyze how social networks split into factions led by rival leaders, revealing polarization and size scaling behaviors in complex networks like political blogs.

Contribution

The paper presents a novel algorithm for studying network partitions driven by rival leaders, combining numerical simulations and mean-field theory to uncover scaling laws and polarization effects.

Findings

Large network fragments scale with the square root of initial size.

Fragments tend to be polarized, corresponding to political affiliations.

The model successfully applied to real political blog data.

Abstract

A model algorithm is proposed to study subsequent partitions of complex networks describing social structures. The partitions are supposed to appear as actions of rivaling leaders corresponding to nodes with large degrees. The condition of a partition is that the distance between two leaders is at least three links. This ensures that the layer of nearest neighbours of each leader remains attached to him. As a rule, numerically calculated size distribution of fragments of scale-free Albert-Barabasi networks reveals one large fragment which contains the original leader (hub of the network), and a number of small fragments with opponents that are described by two Weibull distributions. Numerical simulations and mean-field theory reveal that size of the larger fragment scales as the square root of the initial network size. The algorithm is applied to the data on political blogs in U.S. (L. Adamic and N. Glance, Proc. WWW-2005). The obtained fragments are clearly polarized; either they belong to Democrats, or to the GOP.