Evolving networks by merging cliques

Kazuhiro Takemoto, Chikoo Oosawa

Published 2005-10-18, updated 2005-11-22Version 2

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.