Evolving networks consist of cliques

TL;DR

This paper introduces a recursive model for evolving networks composed of cliques, demonstrating they exhibit scale-free, small-world properties with tunable degree exponents and analytically derived clustering coefficients.

Contribution

The paper presents a novel recursive algorithm for constructing clique-based scale-free networks with analytical solutions for degree distribution and clustering.

Findings

Networks follow a power-law degree distribution with exponents between 2 and 3.

Networks exhibit small-world characteristics.

Analytical expressions for clustering coefficients are derived.

Abstract

Many real networks have cliques as their constitutional units. Here we present a family of scale-free network model consist of cliques, which is established by a simple recursive algorithm. We investigate the networks both analytically and numerically. The obtained analytical solution shows that the networks follow a power-law degree distribution, with degree exponent continuously tuned between 2 and 3, coinciding with the empirically found results. The exact expression of clustering coefficient is also provided for the networks. Furthermore, the investigation of the average path length reveals that the networks possess small-world feature.