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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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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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.
AbstractList	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.
Author	Maletić, S. Rajković, M.
Author_xml	– sequence: 1 givenname: S. surname: Maletić fullname: Maletić, S. email: supersloba@vinca.rs organization: Institute of Nuclear Sciences Vinča, University of Belgrade – sequence: 2 givenname: M. surname: Rajković fullname: Rajković, M. organization: Institute of Nuclear Sciences Vinča, University of Belgrade
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Title	Combinatorial Laplacian and entropy of simplicial complexes associated with complex networks
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