Abstract
One of the more challenging tasks in the understanding of dynamical
properties of models on top of complex networks is to capture the precise role
of multiplex topologies. In a recent paper, Gomez et al. Phys. Rev. Lett. 101,
028701 (2013) proposed a framework for the study of diffusion processes in
such networks. Here, we extend the previous framework to deal with general
configurations in several layers of networks, and analyze the behavior of the
spectrum of the Laplacian of the full multiplex. We derive an interesting
decoupling of the problem that allow us to unravel the role played by the
interconnections of the multiplex in the dynamical processes on top of them.
Capitalizing on this decoupling we perform an asymptotic analysis that allow us
to derive analytical expressions for the full spectrum of eigenvalues. This
spectrum is used to gain insight into physical phenomena on top of multiplex,
specifically, diffusion processes and synchronizability.
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