Do extremists impose the structure of social networks?

TL;DR

This paper models social network formation by assigning nodes features and affinities, demonstrating that extremists with high affinity values shape the network's degree distribution and overall topology.

Contribution

It introduces a model where extremists influence network structure, showing their dominant role in shaping topology through affinity-based connection rules.

Findings

Networks exhibit power-law degree distributions influenced by extremists.

Extremists determine the network's degree distribution tail.

The model has implications for social network analysis and epidemiology.

Abstract

The structure and the properties of complex networks essentially depend on the way how nodes get connected to each other. We assume here that each node has a feature which attracts the others. We model the situation by assigning two numbers to each node, \omega and \alpha, where \omega indicates some property of the node and \alpha the affinity towards that property. A node A is more likely to establish a connection with a node B if B has a high value of \omega and A has a high value of \alpha. Simple computer simulations show that networks built according to this principle have a degree distribution with a power law tail, whose exponent is determined only by the nodes with the largest value of the affinity \alpha (the "extremists"). This means that the extremists lead the formation process of the network and manage to shape the final topology of the system. The latter phenomenon may have implications in the study of social networks and in epidemiology.