Statistical properties of random clique networks

TL;DR

This paper introduces a random clique network model that captures high clustering and modularity in complex networks, revealing unique behaviors in clustering and degree distributions compared to Erdős-Rényi networks.

Contribution

The paper proposes a novel random clique network model combining ER rules and cliques, explaining its properties and differences from traditional models.

Findings

Small average degree networks have high clustering and power-law spectra.

High average degree networks resemble ER networks.

Clustering coefficient varies non-monotonically with degree.

Abstract

In this paper, a random clique network model to mimic the large clustering coefficient and the modular structure that exist in many real complex networks, such as social networks, artificial networks, and protein interaction networks, is introduced by combining the random selection rule of the Erd\"os and R\'enyi (ER) model and the concept of cliques. We find that random clique networks having a small average degree differ from the ER network in that they have a large clustering coefficient and a power law clustering spectrum, while networks having a high average degree have similar properties as the ER model. In addition, we find that the relation between the clustering coefficient and the average degree shows a non-monotonic behavior and that the degree distributions can be fit by multiple Poisson curves; we explain the origin of such novel behaviors and degree distributions.