An evolving network model with modular growth

TL;DR

This paper introduces a new evolving network model that grows through modular units, combining small-world and scale-free properties, with analytical and numerical validation of its structural characteristics.

Contribution

It presents a novel modular growth model for networks, analyzing its degree distribution, clustering, and small-world features through theoretical and simulation methods.

Findings

Degree distribution exhibits small-world and scale-free features

Network maintains small-world properties despite randomness in module addition

Modularity can be tuned by adjusting intra- and inter-module edge ratios

Abstract

In this paper, we propose an evolving network model growing fast in units of module, based on the analysis of the evolution characteristics in real complex networks. Each module is a small-world network containing several interconnected nodes, and the nodes between the modules are linked by preferential attachment on degree of nodes. We study the modularity measure of the proposed model, which can be adjusted by changing ratio of the number of inner-module edges and the number of inter-module edges. Based on the mean field theory, we develop an analytical function of the degree distribution, which is verified by a numerical example and indicates that the degree distribution shows characteristics of the small-world network and the scale-free network distinctly at different segments. The clustering coefficient and the average path length of the network are simulated numerically, indicating that the network shows the small-world property and is affected little by the randomness of the new module.