Tuning the average path length of complex networks and its influence to the emergent dynamics of the majority-rule model

TL;DR

This paper presents a method to precisely control the average path length of complex networks through rewiring, and demonstrates how this influences the emergent behavior of the majority-rule model.

Contribution

It introduces a novel rewiring algorithm using Metropolis Monte Carlo to tune the average path length while maintaining other network properties.

Findings

Rewiring can effectively modify the average path length without altering degree and clustering.

The emergent dynamics of the majority-rule model are significantly affected by changes in the average path length.

The method enables systematic exploration of network topology effects on dynamics.

Abstract

We show how appropriate rewiring with the aid of Metropolis Monte Carlo computational experiments can be exploited to create network topologies possessing prescribed values of the average path length (APL) while keeping the same connectivity degree and clustering coefficient distributions. Using the proposed rewiring rules we illustrate how the emergent dynamics of the celebrated majority-rule model are shaped by the distinct impact of the APL attesting the need for developing efficient algorithms for tuning such network characteristics.