Multiplexity versus correlation: the role of local constraints in real multiplexes

TL;DR

This paper investigates how local heterogeneity constraints influence the measurement of dependencies in multiplex networks, showing that traditional correlation metrics can be misleading without accounting for degree and strength distributions.

Contribution

It introduces novel multiplexity measures that incorporate heterogeneity constraints, improving the accuracy of dependency assessments in real-world multiplex networks.

Findings

Homogeneous benchmarks can misrepresent layer dependencies.

Heterogeneity in degree and strength distributions significantly affects multiplexity.

Distribution of hubs across layers plays a crucial role in network dependencies.

Abstract

Several real-world systems can be represented as multi-layer complex networks, i.e. in terms of a superposition of various graphs, each related to a different mode of connection between nodes. Hence, the definition of proper mathematical quantities aiming at capturing the level of complexity of those systems is required. Various attempts have been made to measure the empirical dependencies between the layers of a multiplex, for both binary and weighted networks. In the simplest case, such dependencies are measured via correlation-based metrics: we show that this is equivalent to the use of completely homogeneous benchmarks specifying only global constraints, such as the total number of links in each layer. However, these approaches do not take into account the heterogeneity in the degree and strength distributions, which are instead a fundamental feature of real-world multiplexes. In this work, we compare the observed dependencies between layers with the expected values obtained from reference models that appropriately control for the observed heterogeneity in the degree and strength distributions. This leads to novel multiplexity measures that we test on different datasets, i.e. the International Trade Network (ITN) and the European Airport Network (EAN). Our findings confirm that the use of homogeneous benchmarks can lead to misleading results, and furthermore highlight the important role played by the distribution of hubs across layers.