Weighted multiplex networks.

Giulia Menichetti,Daniel Remondini,Ginestra Bianconi,Pietro Panzarasa,Raúl J Mondragón,Yamir Moreno

doi:10.1371/journal.pone.0097857

Giulia Menichetti, Daniel Remondini + Show 4 more

Open Access

https://doi.org/10.1371/journal.pone.0097857

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Abstract

One of the most important challenges in network science is to quantify the information encoded in complex network structures. Disentangling randomness from organizational principles is even more demanding when networks have a multiplex nature. Multiplex networks are multilayer systems of nodes that can be linked in multiple interacting and co-evolving layers. In these networks, relevant information might not be captured if the single layers were analyzed separately. Here we demonstrate that such partial analysis of layers fails to capture significant correlations between weights and topology of complex multiplex networks. To this end, we study two weighted multiplex co-authorship and citation networks involving the authors included in the American Physical Society. We show that in these networks weights are strongly correlated with multiplex structure, and provide empirical evidence in favor of the advantage of studying weighted measures of multiplex networks, such as multistrength and the inverse multiparticipation ratio. Finally, we introduce a theoretical framework based on the entropy of multiplex ensembles to quantify the information stored in multiplex networks that would remain undetected if the single layers were analyzed in isolation.

Highlights

Network theory investigates the global topology and structural patterns of the interactions among the constituent elements of a number of complex systems including social groups, infrastructure and technological systems, the brain and biological networks [1,2,3,4]
To provide empirical evidence that weighted properties of multilinks are fundamental for properly assessing weighted multiplex networks, we focus on the networks of the authors of papers published in the journals of the American Physical Society (APS), and analyze the scientific collaboration network and the citation network connecting the same authors
We have shown that weighted multiplex networks are characterized by significant correlations across layers, and in particular that weights are closely correlated with the multiplex network structure

Summary

Introduction

Network theory investigates the global topology and structural patterns of the interactions among the constituent elements of a number of complex systems including social groups, infrastructure and technological systems, the brain and biological networks [1,2,3,4]. To provide empirical evidence that weighted properties of multilinks are fundamental for properly assessing weighted multiplex networks, we focus on the networks of the authors of papers published in the journals of the American Physical Society (APS), and analyze the scientific collaboration network and the citation network connecting the same authors. These networks are intrinsically weighted since any two scientists can co-author more than one paper and can cite each other’s work several times. Based on the entropy of multiplex ensembles, we propose an indicator J to evaluate the additional amount of information that can be extracted from the weighted properties of multilinks in multiplex networks over the information encoded in the properties of their individual layers analyzed separately

Definition A weighted multiplex network is a set of M weighted networks

Assessing the Informational Content of Weighted

Conclusions

Materials and Methods