title: Structural measures for multiplex networks.
abstract: Many real-world complex systems consist of a set of elementary units connected by relationships of different kinds. All such systems are better described in terms of multiplex networks, where the links at each layer represent a different type of interaction between the same set of nodes rather than in terms of (single-layer) networks. In this paper we present a general framework to describe and study multiplex networks, whose links are either unweighted or weighted. In particular, we propose a series of measures to characterize the multiplexicity of the systems in terms of (i) basic node and link properties such as the node degree, and the edge overlap and reinforcement, (ii) local properties such as the clustering coefficient and the transitivity, and (iii) global properties related to the navigability of the multiplex across the different layers. The measures we introduce are validated on a genuinely multiplex data set of Indonesian terrorists, where information among 78 individuals are recorded with respect to mutual trust, common operations, exchanged communications, and business relationships.
authors.affiliation: School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom.
authors.forename: Federico
authors.initials: F
authors.lastname: Battiston
authors.affiliation: School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom and Laboratorio sui Sistemi Complessi, Scuola Superiore di Catania, I-95123 Catania, Italy.
authors.forename: Vincenzo
authors.initials: V
authors.lastname: Nicosia
authors.affiliation: School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom and Laboratorio sui Sistemi Complessi, Scuola Superiore di Catania, I-95123 Catania, Italy and Dipartimento di Fisica ed Astronomia, Università di Catania and INFN, I-95123 Catania, Italy.
authors.forename: Vito
authors.initials: V
authors.lastname: Latora