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

TL;DR

This paper introduces new clustering coefficients for weighted, directed multilayer networks, extending existing concepts to better analyze complex systems like international trade networks.

Contribution

It provides novel definitions of clustering coefficients for multilayer networks and demonstrates their effectiveness on the international trade network.

Findings

Coefficients successfully describe complex multilayer interactions.

They help disentangle effects of countries and sectors.

Application reveals insights into trade network structure.

Abstract

In this paper, we provide novel definitions of clustering coefficient for weighted and directed multilayer networks. We extend in the multilayer theoretical context the clustering coefficients proposed in the literature for weighted directed monoplex networks. We quantify how deeply a node is involved in a choesive structure focusing on a single node, on a single layer or on the entire system. 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.