Combinatorial Laplacian and entropy of simplicial complexes associated with complex networks
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.
Source:
European Physical Journal : Special Topics, 2012, 212, 1, 77-97Funding / projects:
- Advanced analytical, numerical and analysis methods of applied fluid mechanics and complex systems (RS-MESTD-Basic Research (BR or ON)-174014)
DOI: 10.1140/epjst/e2012-01655-6
ISSN: 1951-6355
WoS: 000308723800006
Scopus: 2-s2.0-84866499024
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Institution/Community
VinčaTY - JOUR AU - Maletić, Slobodan AU - Rajković, Milan PY - 2012 UR - https://vinar.vin.bg.ac.rs/handle/123456789/5035 AB - 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. T2 - European Physical Journal : Special Topics T1 - Combinatorial Laplacian and entropy of simplicial complexes associated with complex networks VL - 212 IS - 1 SP - 77 EP - 97 DO - 10.1140/epjst/e2012-01655-6 ER -
@article{ author = "Maletić, Slobodan and Rajković, Milan", year = "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.", journal = "European Physical Journal : Special Topics", title = "Combinatorial Laplacian and entropy of simplicial complexes associated with complex networks", volume = "212", number = "1", pages = "77-97", doi = "10.1140/epjst/e2012-01655-6" }
Maletić, S.,& Rajković, M.. (2012). Combinatorial Laplacian and entropy of simplicial complexes associated with complex networks. in European Physical Journal : Special Topics, 212(1), 77-97. https://doi.org/10.1140/epjst/e2012-01655-6
Maletić S, Rajković M. Combinatorial Laplacian and entropy of simplicial complexes associated with complex networks. in European Physical Journal : Special Topics. 2012;212(1):77-97. doi:10.1140/epjst/e2012-01655-6 .
Maletić, Slobodan, Rajković, Milan, "Combinatorial Laplacian and entropy of simplicial complexes associated with complex networks" in European Physical Journal : Special Topics, 212, no. 1 (2012):77-97, https://doi.org/10.1140/epjst/e2012-01655-6 . .