Emergence of large cliques in random scale-free networks
Bianconi, Ginestra and Marsili, Matteo (2005) Emergence of large cliques in random scale-free networks. Working Paper. Coventry: Warwick Business School, Financial Econometrics Research Centre. Working papers (Warwick Business School. Financial Econometrics Research Centre) (No.05-).
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In a network cliques are fully connected subgraphs that reveal which are the tight communities present in it. Cliques of size c > 3 are present in random Erdös and Renyi graphs only in the limit of diverging average connectivity. Starting from the finding that real scale free graphs have large cliques, we study the clique number in uncorrelated scale-free networks finding both upper and lower bounds. Interesting we find that in scale-free networks large cliques appear also when the average degree is finite, i.e. even for networks with power-law degree distribution exponents ! ! (2, 3). Moreover as long as ! < 3 scale-free networks have a maximal clique which diverges with the system size.
|Item Type:||Working or Discussion Paper (Working Paper)|
|Subjects:||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):||Cliques (Sociology), Subgroup growth (Mathematics), Graph theory, Maximal subgroups, Distribution (Economic theory)|
|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:||12 October 2005|
|Number of Pages:||9|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
 R. Albert and A.-L. Barabeási, Rev. Mod. Phys. 74, 47
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