Effects of degree correlations on the loop structure of scale free networks
Bianconi, Ginestra and Marsili, Matteo (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) (No.06-).
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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|
|Official Date:||14 July 2006|
|Number of Pages:||13|
|Institution:||University of Warwick|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
|Funder:||Sixth Framework Programme (European Commission) (FP6)|
 R. Albert and A.-L. Barabeási, Rev. Mod. Phys. 74, 47
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