title: Combinatorial study of degree assortativity in networks.
abstract: 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.
authors.affiliation: Department of Mathematics and Statistics, SUPA and Institute of Complex Systems, University of Strathclyde, Glasgow G1 1XQ, United Kingdom.
authors.forename: Ernesto
authors.initials: E
authors.lastname: Estrada