A tensor-based unified approach for clustering coefficients in financial multiplex networks

Abstract

Complex systems in the real world are frequently characterized by entities connected by relationships of different nature. These systems can be appropriately described by multilayer networks where the different relations between nodes can be conveniently expressed structuring the network through different layers. To extend in a multilayer context the classical network indicators proposed for monolayer networks is an important issue. In this work we study the incidence of triangular patterns expressed through the local clustering coefficient in a weighted undirected multilayer network. We provide new local clustering coefficients for multilayer networks, looking at the network from different perspectives depending on the node's position, as well as a global clustering coefficient for the whole network. We also prove that all the well-known expressions for clustering coefficients existing in the literature, suitably extended to the multilayer framework, may be unified into our proposal, both in terms of tensors and supradjacency matrix. To show the effectiveness of the proposed measures, we study an application to the multilayer temporal financial network based on the returns of the S&P100 assets.