Ultrametric graphons model hierarchical community networks and yield closed-form Laplacian spectra that approximate those of sampled random graphs with high probability as hierarchy depth grows.
A comprehensive review of community detection in graphs , year =
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Explicit formulas for intrinsic volumes of ℓ_p-balls via one-dimensional integrals with special function F_p, plus Maxwell-Poincaré-Borel limit laws for curvature measures in high dimensions.
A literature survey that proposes a multidimensional taxonomy for community detection, introduces a general mathematical formalization accommodating disjoint/overlapping/fuzzy structures, reviews modularity functions and both algorithmic and mathematical programming methods, and discusses benchmark
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Ultrametric Graphons and Hierarchical Community Networks: Spectral Theory and Applications
Ultrametric graphons model hierarchical community networks and yield closed-form Laplacian spectra that approximate those of sampled random graphs with high probability as hierarchy depth grows.
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Intrinsic volumes of $\ell_p$-balls and a continuum of Maxwell--Poincar\'e--Borel laws for their curvature measures
Explicit formulas for intrinsic volumes of ℓ_p-balls via one-dimensional integrals with special function F_p, plus Maxwell-Poincaré-Borel limit laws for curvature measures in high dimensions.
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A Survey of Community Detection from an Operations Research Perspective: Taxonomy, Mathematical Formulations, Modularity Functions, and Benchmark Datasets
A literature survey that proposes a multidimensional taxonomy for community detection, introduces a general mathematical formalization accommodating disjoint/overlapping/fuzzy structures, reviews modularity functions and both algorithmic and mathematical programming methods, and discusses benchmark