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Partitioning and modularity of graphs with arbitrary degree distribution

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arxiv cond-mat/0606295 v2 pith:APEVJB4C submitted 2006-06-12 cond-mat.dis-nn cond-mat.stat-mech

classification cond-mat.dis-nncond-mat.stat-mech
keywords graphsdegreedistributionproblemarbitraryfindmodularityphys
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We 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.

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  1. Community Detection in Energy Networks based on Energy Self-Sufficiency and Dynamic Flexibility Activation

    cs.SI 2025-06 conditional novelty 6.0 of 10

    The paper defines energy modularity, a self-sufficiency-based community detection objective, and a scalable Louvain algorithm that optimizes it with flexibility activation.

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