Eur. Phys. J. Special Topics 212, 77-97 (2012)
https://doi.org/10.1140/epjst/e2012-01655-6

Regular Article

Combinatorial Laplacian and entropy of simplicial complexes associated with complex networks

Institute of Nuclear Sciences Vinča, University of Belgrade, PO Box 522, 11001 Belgrade, Serbia

^a e-mail: supersloba@vinca.rs
^b e-mail: milanr@vinca.rs

Received: 31 May 2012
Revised: 23 July 2012
Published online: 17 September 2012

Abstract

Simplicial complexes represent useful and accurate models of complex networks and complex systems in general. We explore the properties of spectra of combinatorial Laplacian operator of simplicial complexes and show its relationship with connectivity properties of the Q-vector and with connectivities of cliques in the simplicial clique complex. We demonstrate the need for higher order analysis in complex networks and compare the results with ordinary graph spectra. Methods and results are obtained using social network of the Zachary karate club.