Competitive cluster growth in complex networks

TL;DR

This paper introduces a model for competitive cluster growth in complex networks, revealing how network topology influences cluster size distribution and its similarity to electoral vote distributions.

Contribution

The study presents a novel idealized model linking cluster growth dynamics to network topology, especially hierarchical networks, and relates findings to electoral vote distributions.

Findings

Cluster size distribution depends on network topology.

Hierarchical networks produce scale-invariant cluster distributions.

Similarity between cluster distributions and electoral vote patterns.

Abstract

Understanding the process by which the individuals of a society make up their minds and reach opinions about different issues can be of fundamental importance. In this work we propose an idealized model for competitive cluster growth in complex networks. Each cluster can be thought as a fraction of a community that shares some common opinion. Our results show that the cluster size distribution depends on the particular choice for the topology of the network of contacts among the agents. As an application, we show that the cluster size distributions obtained when the growth process is performed on hierarchical networks, e.g., the Apollonian network, have a scaling form similar to what has been observed for the distribution of number of votes in an electoral process. We suggest that this similarity is due to the fact that social networks involved in the electoral process may also posses an underlining hierarchical structure.