Rank-based assortativity for weighted, directed networks

Abstract Assortativity measures the tendency of a vertex to bond with another based on their structural or functional features. The assortativity coefficient was originally proposed to specify the node degree–degree correlation for unweighted, undirected networks. This paper proposes a class of rank-based assortativity measures for weighted, directed networks, building upon and extending the work of Litvak and van der Hofstad. These new measures offer improved robustness to variations in edge weights, particularly in networks with extreme-valued edges, by reducing sensitivity to outliers in node connectivity patterns. Extensive simulation studies, based on the Erdös–Rényi random network model and preferential attachment random networks, are employed to compare the robustness of the proposed measures with existing assortativity measures. Finally, the proposed assortativity measures are applied to the networks generated from the World Input–Output Database, yielding insights that differ significantly from those obtained through existing methods.