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

In this paper, we provide novel definitions of clustering coefficient for weighted and directed multilayer networks. We extend in the multilayer theoretical context the clus-tering coefficients proposed in the literature for weighted directed monoplex networks. We quantify how deeply a node is involved in a cohesive structure focusing on a single node, a single layer or the entire system, respectively. The coefficients convey several characteristics inherent to the complex topology of the multilayer 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 multilayer 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. (c) 2022 Elsevier B.V. All rights reserved.

Automated summary

In this paper, new definitions of clustering coefficient for weighted and directed multilayer networks are provided. The clustering coefficients proposed in the literature for weighted directed monoplex networks are extended in the multilayer theoretical context. The coefficients quantify the depth of a node's involvement in a cohesive structure, focusing on a single node, a single layer, or the entire system, respectively. The coefficients convey several characteristics inherent to the complex topology of the multilayer network. Their effectiveness is tested by applying them to the international trade network, which is a particularly complex structure. The coefficients successfully describe the interrelations of the trade network, allowing for the analysis of the effects of countries and sectors and their interactions.