Structural measures for multiplex networks.

By Federico Battiston, Vincenzo Nicosia, Vito Latora. Physical review. E, Statistical, nonlinear, and soft matter physics, 2013

664 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ec4f9d739402c135e171e58bda2ccf5b6364f093

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Citations in the corpus

Contact Patterns in a High School: A Comparison between Data Collected Using Wearable Sensors, Contact Diaries and Friendship Surveys (2015, background): “Fig 9(a) reports in a matrix form the conditional probability to observe a link between two students in a layer of the multiplex, given that the two students are linked in another layer [42].”
Multilayer networks (2013, methodology): “One can define a multiplex network, a multirelational network and similar types of multilayer networks as a sequence of graphs [2,72,73,75,83]: {Gα}α=1 = {(Vα , Eα)}α=1, where Eα ⊆ Vα × Vα is the set of edges and α indexes the graphs.”
Networks beyond pairwise interactions: structure and dynamics (2020, background): “edge overlap [564]), and the beneficial effects of multiplexity completely disappear when the overlap between the network structures goes to zero, no matter the number of layers [565].”
Multilayer Analysis and Visualization of Networks (2014, background): “For example, there have been numerous studies to attempt to understand how interdependencies (e.g., [37, 38]), multilayer structures (e.g., [39, 40]), dynamics (e.g., [41, 42]), and control (e.g., [43]) can improve understanding of complex interacting systems.”
A Novel Multiplex Network-Based Sensor Information Fusion Model and Its Application to Industrial Multiphase Flow System (2018, background): “Moreover, because of the multiplex character of realworld systems, the interest of complex network has gradually changed from single-layer network to multilayer network [29], especially multiplex networks [30]-[32].”
The structure and dynamics of multilayer networks (2014, background): “However, different types of reachability may be considered [20,23] depending, for example, on whether we are considering only the edges included in some layers.”
The time-evolving epileptic brain network: concepts, definitions, accomplishments, perspectives (2024, background): “Despite a continuous development of metrics to characterize such a network of networks (Battiston et al., 2014; De Domenico et al., 2015; Nicosia and Latora, 2015; Iacovacci and Bianconi, 2016; Ghariblou et al., 2017; Mandke et al., 2018; Tudisco et al., 2018; Zaoli et al., 2021), applications in…”