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

¹ Department of Biological Physics, Eötvös University Pázmány P. stny. 1A, H-1117 Budapest, Hungary
² Biological Physics Research Group of HAS, Eötvös University Pázmány P. stny. 1A, H-1117 Budapest, Hungary

Received: 3 November 2005
Accepted: 8 December 2005

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.