Multiplex networks of musical artists: the effect of heterogeneous inter-layer links

TL;DR

This paper investigates how heterogeneous inter-layer link weights in multiplex networks of musicians influence structural properties, revealing a transition in algebraic connectivity that differs from classical homogeneous models.

Contribution

It introduces a model for multiplex networks with non-uniform inter-layer link weights based on empirical data, highlighting the impact of heterogeneity on network structure.

Findings

Heterogeneous inter-layer weights significantly affect algebraic connectivity.

Transition in network properties differs from classical homogeneous models.

Empirical data-based modeling enhances understanding of real multiplex networks.

Abstract

The way the topological structure goes from a decoupled state into a coupled one in multiplex networks has been widely studied by means of analytical and numerical studies, involving models of artificial networks. In general, these experiments assume uniform interconnections between layers offering, on the one hand, an analytical treatment of the structural properties of multiplex networks but, on the other hand, loosing applicability to real networks where heterogeneity of the links' weights is an intrinsic feature. In this paper, we study 2-layer multiplex networks of musicians whose layers correspond to empirical datasets containing, and linking the information of: (i) collaboration between them and (ii) musical similarities. In our model, connections between the collaboration and similarity layers exist, but they are not ubiquitous for all nodes. Specifically, inter-layer links are created (and weighted) based on structural resemblances between the neighborhood of an artist, taking into account the level of interaction at each layer. Next, we evaluate the effect that the heterogeneity of the weights of the inter-layer links has on the structural properties of the whole network, namely the second smallest eigenvalue of the Laplacian matrix (algebraic connectivity). Our results show a transition in the value of the algebraic connectivity that is far from classical theoretical predictions where the weight of the inter-layer links is considered to be homogeneous.