Partitioning and modularity of graphs with arbitrary degree distribution

dc.creatorReichardt, Joerg
dc.creatorBornholdt, Stefan
dc.date2006-06-12
dc.date2007-04-06
dc.date.accessioned2026-07-07T12:11:45Z
dc.date.available2026-07-07T12:11:45Z
dc.descriptionWe solve the graph bi-partitioning problem in dense graphs with arbitrary degree distribution using the replica method. We find the cut-size to scale universally with <k^1/2>. In contrast, earlier results studying the problem in graphs with a Poissonian degree distribution had found a scaling with <k>^1/2 [Fu and Anderson, J. Phys. A: Math. Gen. 19, 1986]. The new results also generalize to the problem of q-partitioning. They can be used to find the expected modularity Q [Newman and Grivan, Phys. Rev. E, 69, 2004] of random graphs and allow for the assessment of statistical significance of the output of community detection algorithms.
dc.descriptionRevised version including new plots and improved discussion of some mathematical details
dc.identifierhttps://arxiv.org/abs/cond-mat/0606295
dc.identifierhttp://arxiv.org/abs/cond-mat/0606295
dc.identifierPhys. Rev. E 76, 015102(R) (2007)
dc.identifierdoi:10.1103/PhysRevE.76.015102
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/210323
dc.subjectDisordered Systems and Neural Networks
dc.subjectStatistical Mechanics
dc.titlePartitioning and modularity of graphs with arbitrary degree distribution
dc.typetext

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