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Phys Rev Lett. 2013 Jan 11;110(2):028701. Epub 2013 Jan 8.

Diffusion dynamics on multiplex networks.

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Departament d'Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain.


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.

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