Triadic closure as a basic generating mechanism of communities in complex networks

TL;DR

This paper demonstrates that simple triadic closure mechanisms in network growth models naturally produce community structures, high clustering, and fat-tailed degree distributions, revealing universal properties of complex networks.

Contribution

It introduces a model based on triadic closure that explains the spontaneous emergence of communities and other universal network properties.

Findings

Communities emerge from stochastic heterogeneity and grow through a cycle of growth and fragmentation.

Community structures are more pronounced in sparser graphs and diminish with increased density and randomness.

A phase transition occurs with fitness-based attachment, leading to mesoscopic organization and superhubs.

Abstract

Most of the complex social, technological and biological networks have a significant community structure. Therefore the community structure of complex networks has to be considered as a universal property, together with the much explored small-world and scale-free properties of these networks. Despite the large interest in characterizing the community structures of real networks, not enough attention has been devoted to the detection of universal mechanisms able to spontaneously generate networks with communities. Triadic closure is a natural mechanism to make new connections, especially in social networks. Here we show that models of network growth based on simple triadic closure naturally lead to the emergence of community structure, together with fat-tailed distributions of node degree, high clustering coefficients. Communities emerge from the initial stochastic heterogeneity in the concentration of links, followed by a cycle of growth and fragmentation. Communities are the more pronounced, the sparser the graph, and disappear for high values of link density and randomness in the attachment procedure. By introducing a fitness-based link attractivity for the nodes, we find a novel phase transition, where communities disappear for high heterogeneity of the fitness distribution, but a new mesoscopic organization of the nodes emerges, with groups of nodes being shared between just a few superhubs, which attract most of the links of the system.