engleski

Percolation Theory for Color Diversity on Random Networks

As a powerful but bare generalization of complex systems, network has typically been abstracted in previous percolation studies as a set of identical objects connected with identical kind of bonds. Recently, it was shown that the colored network, in which the color is an additional degree of freedom allocated to every either site or bond, is a more sensible representation of complex system subject to different classes of vulnerabilities. To quantify how network structure has effect on the diversity of classes (different number of colors and color distributions), we study the color-avoiding component, which nodes stay connected even when the extinction of any particular color occurs, and present the condition for existence of this component in a given network. We use a specified version of percolation theory which takes into account the sensibility of network to the disconnection of hole class of one color -- the color-avoiding percolation. Here we provide analytical and numerical evidence of a color affected mean- field critical behavior for a class of networks. To the contrary, we also find that the critical behavior stays color independent in networks defined with the long-tail degree distribution.

percolation ; phase transition on network ; color graph ; avoiding vulnerabilities

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