S. Gomez, A. Diaz-Guilera, J. Gomez-Gardeñes, C. J. Perez-Vicente, Y. Moreno, A. Arenas
We study the time scales associated to diffusion processes that take place on multiplex networks (a set of networks structured in 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 diffusion-like processes on top of multiplex networks.
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http://arxiv.org/abs/1207.2788
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