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Combinatorial study of degree assortativity in networks

Estrada, Ernesto (2011) Combinatorial study of degree assortativity in networks. Physical Review E, 84. 047101. ISSN 1539-3755

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Why are some networks degree-degree correlated (assortative), while most of the real-world ones are anticorrelated (disassortative)? Here, we prove, by combinatorial methods, that the assortativity of a network depends only on three structural factors: transitivity (clustering coefficient), intermodular connectivity, and branching. Then, a network is assortative if the contributions of the first two factors are larger than that of the third. Highly branched networks are likely to be disassortative.