Diffusion dynamics on multiplex networks

By Sergio Gómez, Albert Díaz-Guilera, Jesús Gómez-Gardeñes, C. P. Vicente, Yamir Moreno, Alex Arenas. Physical Review Letters, 2012

847 citations recorded by the source corpus.

We study the time scales associated with diffusion processes that take place on multiplex networks, i.e., on a set of networks linked through interconnected layers. To this end, we propose the construction of a supra-laplacian matrix, which consists of a dimensional lifting of the laplacian matrix of each layer of the multiplex network. We use perturbative analysis to reveal analytically the structure of eigenvectors and eigenvalues of the complete network in terms of the spectral properties of the individual layers. The spectrum of the supra-laplacian allows us to understand the physics of diffusionlike processes on top of multiplex networks.

Subfields: Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/11bd53947535d1ba6d31d019b1446c2bf25485d1

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In Computer Networks and Communications

In Statistical and Nonlinear Physics

Citations in the corpus

Complex network approaches to nonlinear time series analysis (2019, background): “Multiplex and multilayer networks explicitly incorporate multiple levels of social interactions and have been successfully applied to the study of disease spreading and diffusion dynamics [87,88] or the evolution of cooperation in the presence of social dilemmas [89].”
Coupled disease–behavior dynamics on complex networks: A review (2015, background): “The broad applicability of multilayer networks and their success in providing insight into the structure and dynamics of realistic systems have thus generated considerable excitement [105] [106] [107] [108] [109] .”
Synchronization in complex networks and its application - A survey of recent advances and challenges (2014, background): “Consider the following multiplex network composed of M layers (Gómez et al., 2013; Radicchi & Arenas, 2013): _xmi ¼ Dm XN j¼1 wmij x m j xmi þ XM h¼1 Dmh xhi xmi ; ð22Þ where wmij denotes the weight matrix at layer m (w m ij ¼ 0 meaning that there is no link between nodes i and j in layer m); Dm is…”
The structure and dynamics of multilayer networks (2014, background): “[45], in which simple linear diffusion is generalized to the case of multiplex networks.”
Navigability of interconnected networks under random failures (2013, background): “i; j=1 Δije−Ci; jð1Þt−Ci;jð2Þλ −1 2 ; [3]”
Human mobility: Models and applications (2017, methodology): “The more intricate topology of multilayer networks necessarily affects the spreading processes taking place on the system (diffusion and navigation) [205, 206, 189] that are modeled using the methods discussed in Sec.”
Statistical physics of vaccination (2016, background): “Not surprisingly, multilayer networks have recently been the subject of many novel frameworks to study various dynamical processes, such as epidemic spreading [216, 231, 372, 604], diffusion [342], voting [605], synchronization [606], and the evolution of cooperation in game-theoretical models [607,”
Network resilience (2020, background): “between systems into consideration, many studies have been carried out to study the robustness in interdependent networks [14, 810, 811, 812, 813, 814, 815, 816, 648, 619, 817, 818], interconnected networks [819, 820, 649], multi-layered networks [821, 822, 823, 824, 825], multiplex networks [826], ”