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, 77-97
TY - 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 . .
