Effects of degree correlations on the loop structure of scale free networks
Bianconi, Ginestra and Marsili, Matteo, 1966- (2006) Effects of degree correlations on the loop structure of scale free networks. Working Paper. Coventry: Warwick Business School, Financial Econometrics Research Centre. (Working papers (Warwick Business School. Financial Econometrics Research Centre)).
WRAP_Bianconi_fwp06-16.pdf - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Official URL: http://www2.warwick.ac.uk/fac/soc/wbs/research/wfr...
In this paper we study the impact of degree correlations in the subgraph statistics of scalefree networks. In particular we consider loops, simple cases of network subgraphs which encode the redundancy of the paths passing through every two nodes of the network. We provide an understanding of the scaling of the clustering coefficient in modular networks in terms of the maximal eigenvector of the average adjacency matrix of the ensemble. Furthermore we show that correlations affect in a relevant way the average number of Hamiltonian paths in a three-core of real world networks. We prove our results in the two-vertex correlated hidden variable ensemble and we check the results with exact counting of small loops in real graphs.
|Item Type:||Working or Discussion Paper (Working Paper)|
|Subjects:||H Social Sciences > HB Economic Theory
Q Science > QA Mathematics
|Divisions:||Faculty of Social Sciences > Warwick Business School > Financial Econometrics Research Centre
Faculty of Social Sciences > Warwick Business School
|Library of Congress Subject Headings (LCSH):||Mathematical statistics, Information networks, Scaling laws (Statistical physics), Eigenvectors|
|Series Name:||Working papers (Warwick Business School. Financial Econometrics Research Centre)|
|Publisher:||Warwick Business School, Financial Econometrics Research Centre|
|Place of Publication:||Coventry|
|Date:||14 July 2006|
|Number of Pages:||13|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
|Funder:||Sixth Framework Programme (European Commission) (FP6)|
|References:|| R. Albert and A.-L. Barabeási, Rev. Mod. Phys. 74, 47 (2002).  S. N. Dorogovtsev and J. F. F. Mendes, Evolution of Networks (Oxford University Press, Oxford, 2003).  M. E. J. Newman, SIAM Review 45, 167 (2003).  R. Pastor-Satorras and A. Vespignani, Evolution and Structure of the Internet (Cambridge University Press,Cambridge U.K.,2004).  A.-L. Barabási and R. Albert, Science 286, 509 (1999)  R. Milo, S. Shen-Orr, S. Itzkovitz, N. Kashtan, D. Chklovskii and U. Alon, Science 298, 824 (2002).  A. Vazquez, R. Dobrin, D. Sergi, J.-P. Eckmann, Z. N. Oltvai and A.-L. Barab´asi PNAS 101, 17940 (2004).  S. Janson, T. Luczak and A. Rucinski, Random graphs (John Wiley & Sons,New York, 2000).  G. Bianconi and A. Capocci, Phys. Rev. Lett. 90 ,078701 (2003).  G. Bianconi and M. Marsili, JSTAT P06005 (2005).  J. Berg and M. Lassig Phys. Rev. Lett. 89 (2002).  R. Pastor-Satorras, A. Vazquez and A. Vespignani Phys. Rev. Lett.87, 258701 (2001).  M. E. J. Newman, Phys. Rev. Lett. 89, 208701 (2002).  E. Ravasz, A. L. Somera, D. A. Mongru, Z. N. Oltvai and A.-L. Barab´asi, Science 297, 1551 (2002).  G. Bianconi, G. Caldarelli and A. Capocci, Phys. Rev. E 71, 066116 (2005).  S. N. Soffer and A. Vazquez Phys. Rev. E 71, (2005).  The the Internet datasets are the one collecetd by University of Oregon Route Views project, NLANR and the protein-protein interaction datasets are one listed in DIP database.  E. Marinari, R. Monasson and G. Semerjian, cond-mat/0507525 (2005).  E. Marinari and R. Monasson, JSTAT P09004 (2004).  G Caldarelli, A. Capocci, P. De Los Rios and M. A. Muñoz, Phys. Rev. Lett. 89, 258702 (2002).  M. Boguña and R. Pastor-Satorras, Phys. Rev. E 68 ,036112 (2003).  K.-L. Goh, B. Kahng and D. Kim Phys. Rev. Lett. 87, 278701 (2001).|
Actions (login required)