Random matrix analysis of multiplex networks

Raghav, Tanu; Jalan, Sarika

doi:10.1016/j.physa.2021.126457

Cited by 7 publications

(2 citation statements)

References 69 publications

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“…Investigating such interconnectivity or inter-layer connections is essential for studying the role of dynamical switching between layers in a multiplex system. These inter-layer connections weights, referred to as multiplexing strength, provide a quantitative measure of impacts of dynamical and structural properties of one layer on those of the another layer [15,16]. Various studies on multilayer networks have established the emerging aspects of the interplay between the intra and inter-layer connections of the associated network [17,18].…”

Section: Introductionmentioning

confidence: 99%

Spacing ratio statistics of multiplex directed networks

Raghav

Jalan

2023

New J. Phys.

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Eigenvalues statistics of various many-body systems have been widelystudied using the nearest neighbor spacing distribution under the random matrixtheory framework. Here, we numerically analyze eigenvalue ratio statistics of multiplexnetworks consisting of directed Erd ̋os-R ́enyi random networks layers represented as,first, weighted non-Hermitian random matrices and then weighted Hermitian randommatrices. We report that the multiplexing strength rules the behaviour of averagespacing ratio statistics for multiplexing networks represented by the non-Hermitianand Hermitian matrices, respectively. Additionally, for both these representationsof the directed multiplex networks, the multiplexing strength appears as a guidingparameter for the eigenvector delocalization of the entire system. These results could be important for driving dynamical processes inseveral real-world multilayer systems, particularly, understanding significance of themultiplexing in comprehending network properties.

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Section: Introductionmentioning

confidence: 99%

Spacing ratio statistics of multiplex directed networks

Raghav

Jalan

2023

New J. Phys.

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“…However, it has been increasingly realized that the description of real-world systems using network framework may be more accurate by incorporating higher order interactions [11]. While the small-world phenomenon has been investigated in different aspects of network theory such as temporal networks [12], spatial networks [13], and multilayer networks [14], it has not been explored for hypergraphs.…”

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confidence: 99%

Smallworldness in hypergraphs

Raghav,

Boccaletti,

Jalan

2023

J. Phys. Complex.

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Most real-world networks are endowed with the small-world property, by means of which the maximal distance between any two of their nodes scales logarithmically rather than linearly with their size. The evidence sparkled a wealth of studies trying to reveal possible mechanisms through which the pairwise interactions amongst the units of a network are structured in a way to determine such observedregularity. Here we show that smallworldness occurs also when interactions are of higher order. Namely, by considering Q-uniform hypergraphs and a process through which connections can be randomly rewired with given probability p, we find thatsuch systems may exhibit prominent clustering properties in connection with small average path lengths for a wide range of p values, in analogy to the case of dyadic interactions. The nature of small-world transition remains the same at different ordersQ (=2, 3, 4, 5, 6) of the interactions, however, the increase in the hyperedge order reduces the range of rewiring probability for which smallworldness emerge.

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Robustness measurement of multiplex networks based on graph spectrum

Chen

et al. 2023

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Networks can provide effective representations of the relationships between elements in complex systems through nodes and links. On this basis, relationships between multiple systems are often characterized as multilayer networks (or networks of networks). As a typical representative, a multiplex network is often used to describe a system in which there are many replaceable or dependent relationships among elements in different layers. This paper studies robustness measures for different types of multiplex networks by generalizing the natural connectivity calculated from the graph spectrum. Experiments on model and real multiplex networks show a close correlation between the robustness of multiplex networks consisting of connective or dependent layers and the natural connectivity of aggregated networks or intersections between layers. These indicators can effectively measure or estimate the robustness of multiplex networks according to the topology of each layer. Our findings shed new light on the design and protection of coupled complex systems.

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Random matrix analysis of multiplex networks

Cited by 7 publications

References 69 publications

Spacing ratio statistics of multiplex directed networks

Spacing ratio statistics of multiplex directed networks

Smallworldness in hypergraphs

Robustness measurement of multiplex networks based on graph spectrum

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