Clustering coefficients as measures of the complex interactions in a directed weighted multilayer network

Abstract

In this paper, we propose new definitions of clustering coefficient for weighted and directed multiplex networks. We extend in the multiplex framework the formulas of clustering coefficients existing in the literature for weighted directed monoplex networks. We quantify how deep a node is involved in a cohesive structure focusing on a single layer, all layers or the entire system, respectively. The coefficients capture various features intrinsically related to the complex topology of the multiplex network. We test their effectiveness applying them to a particularly complex structure such as the international trade network. The trade data integrate different aspects and they can be described by a directed and weighted multiplex network, where each layer represents import and export relationships between countries for a given sector. The proposed coefficients find successful application in describing the interrelations of the trade network, allowing to disentangle the effects of countries and sectors and jointly consider the interactions between them.