Combinatorial Laplacian and entropy of simplicial complexes associated with complex networks

Combinatorial Laplacian and entropy of simplicial complexes associated with complex networks

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 connectivitie...

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Bibliographic Details
Published in:The European physical journal. ST, Special topics Vol. 212; no. 1; pp. 77 - 97
Main Authors: Maletić, S., Rajković, M.
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer-Verlag 01-09-2012
Subjects:
Atomic
Classical and Continuum Physics
Condensed Matter Physics
Materials Science
Measurement Science and Instrumentation
Molecular
Optical and Plasma Physics
Physics
Physics and Astronomy
Regular Article
Maximal Clique
Club Member
European Physical Journal Special Topic
Simplicial Complex
Complex Network
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Summary: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.
ISSN:1951-6355
1951-6401
DOI:10.1140/epjst/e2012-01655-6