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Cascading failures in networks with proximate dependent nodes
Yosef Kornbluth1, Steven Lowinger1, Gabriel Cwilich1
1Department of Physics, Yeshiva University, 500 West 185th Street, New York, New York 10033, USA.
Abstract:
We study the mutual percolation of a system composed of two interdependent random regular networks. We introduce a notion of distance to explore the effects of the proximity of interdependent nodes on the cascade of failures after an initial attack. We find a nontrivial relation between the nature of the transition through which the networks disintegrate and the parameters of the system, which are the degree of the nodes and the maximum distance between interdependent nodes. We explain this relation by solving the problem analytically for the relevant set of cases. In the process, we solve a variant of Rényi's parking problem on treelike graphs.
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