Evolving networks by merging cliques

TL;DR

This paper introduces a network evolution model based on merging complete graph modules, producing networks with tunable power-law degree distributions and clustering properties, applicable to various classical network types.

Contribution

The paper presents a novel network growth model using clique merging, demonstrating tunable degree exponents and analytical solutions linking parameters to network topology.

Findings

Networks exhibit power-law degree distributions and clustering spectra.

Degree exponent is tunable via merging node ratios.

Model generalizes the Barabási-Albert model under certain conditions.

Abstract

We propose a model for evolving networks by merging building blocks represented as complete graphs, reminiscent of modules in biological system or communities in sociology. The model shows power-law degree distributions, power-law clustering spectra and high average clustering coefficients independent of network size. The analytical solutions indicate that a degree exponent is determined by the ratio of the number of merging nodes to that of all nodes in the blocks, demonstrating that the exponent is tunable, and are also applicable when the blocks are classical networks such as Erd\H{o}s-R\'enyi or regular graphs. Our model becomes the same model as the Barab\'asi-Albert model under a specific condition.