International Symposium on Nonlinear Theory and Its Applications
Localization of Eigenvectors in Advection Networks
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Advection is a general transport mechanism whereby substances are conveyed by bulk flows. In network-organized systems, advective processes are described by using the advection matrix. Eigenvectors of the advection matrix tend to localize on a subset of network nodes which have similar flow intensities. Although this localization property can be observed numerically in a wide range of networks, no theoretical explanation has been proposed. In this paper, we establish a theoretical approach to explain the localization property on the basis of the perturbation approximation of the advection matrix. We demonstrate the ability of the proposed theory to predict the localizing pattern of eigenvectors for several classes of random networks.