Preferential attachment of communities: the same principle, but a higher level

TL;DR

This paper explores how the network of communities within complex systems grows through a preferential attachment mechanism, similar to individual node networks, and introduces a model for overlapping community dynamics.

Contribution

It demonstrates that community networks develop via preferential attachment and presents a simple model for the evolution of overlapping communities.

Findings

Community network growth follows preferential attachment.

Links between communities are formed through shared members.

A new model describes overlapping community dynamics.

Abstract

The graph of communities is a network emerging above the level of individual nodes in the hierarchical organisation of a complex system. In this graph the nodes correspond to communities (highly interconnected subgraphs, also called modules or clusters), and the links refer to members shared by two communities. Our analysis indicates that the development of this modular structure is driven by preferential attachment, in complete analogy with the growth of the underlying network of nodes. We study how the links between communities are born in a growing co-authorship network, and introduce a simple model for the dynamics of overlapping communities.