Sparse Erdős-Rényi graphs of average degree d have vector chromatic number (1/2)√d + o_d(1).
Spectral redemption in clustering s parse networks
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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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Vector Colorings of Random, Ramanujan, and Large-Girth Irregular Graphs
Sparse Erdős-Rényi graphs of average degree d have vector chromatic number (1/2)√d + o_d(1).
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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