Assortativity measures for weighted and directed networks

Abstract

Abstract Assortativity measures the tendency of a vertex in a network being connected by other vertexes with respect to some vertex-specific features. Classical assortativity coefficients are defined for unweighted and undirected networks with respect to vertex degree. We propose a class of assortativity coefficients that capture the assortative characteristics and structure of weighted and directed networks more precisely. The vertex-to-vertex strength correlation is used as an example, but the proposed measure can be applied to any pair of vertex-specific features. The effectiveness of the proposed measure is assessed through extensive simulations based on prevalent random network models in comparison with existing assortativity measures. In application to World Input–Output Networks, the new measures reveal interesting insights that would not be obtained by using existing ones. An implementation is publicly available in a R package wdnet.