Highly Clustered Complex Networks in the Configuration Model: Random Regular Small-World Network

TL;DR

This paper introduces a method to generate highly clustered random regular networks within the configuration model, demonstrating their small-world properties and analyzing effects on percolation and cooperation dynamics.

Contribution

It presents a novel approach to create highly clustered regular networks and explores their properties, including small-world characteristics and implications for percolation and game theory.

Findings

Highly clustered networks satisfy small-world conditions.

Clustering influences percolation thresholds.

Clustering and heterogeneity affect cooperation levels.

Abstract

We propose a method to make a highly clustered complex network within the configuration model. Using this method, we generated highly clustered random regular networks and analyzed the properties of them. We show that highly clustered random regular networks with appropriate parameters satisfy all the conditions of the small-world network: connectedness, high clustering coefficient, and small-world effect. We also study how clustering affects the percolation threshold in random regular networks. In addition, the prisoner's dilemma game is studied and the effects of clustering and degree heterogeneity on the cooperation level are discussed.