Inhomogeneous evolution of subgraphs and cycles in complex networks

Alexei Vázquez, University of Notre Dame
J. G. Oliveira, University of Notre Dame and Campus Universitário de Santiago
Albert-László Barabási, University of Notre Dame

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Originally published in Physical Review E 71(2), 2005. doi:10.1103/PhysRevE.71.025103

Abstract

Subgraphs and cycles are often used to characterize the local properties of complex networks. Here we show that the subgraph structure of real networks is highly time dependent: as the network grows, the density of some subgraphs remains unchanged, while the density of others increase at a rate that is determined by the network’s degree distribution and clustering properties. This inhomogeneous evolution process, supported by direct measurements on several real networks, leads to systematic shifts in the overall subgraph spectrum and to an inevitable overrepresentation of some subgraphs and cycles.