Evolving small-world scale-free networks consist of cliques

TL;DR

This paper introduces a recursive model for scale-free networks composed of cliques, demonstrating their power-law degree distribution, high clustering, and small-world properties through analytical and numerical analysis.

Contribution

The paper presents a new recursive network model with tunable degree exponent, analytical solutions for clustering, and links to the Yule process, advancing understanding of complex network structures.

Findings

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

Networks exhibit high clustering coefficients.

Networks display small-world characteristics.

Abstract

We present a family of scale-free network model consisting of cliques, which is established by a simple recursive algorithm. We investigate the networks both analytically and numerically. The obtained analytical solutions show that the networks follow a power-law degree distribution, with degree exponent continuously tuned between 2 and 3. 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. Interestingly, we find that a special case of our model can be mapped into the Yule process.