
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 non-trivial 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.
Social and Information Networks (cs.SI), FOS: Computer and information sciences, Physics - Physics and Society, Physics - Data Analysis, Statistics and Probability, FOS: Physical sciences, Computer Science - Social and Information Networks, Physics and Society (physics.soc-ph), Data Analysis, Statistics and Probability (physics.data-an)
Social and Information Networks (cs.SI), FOS: Computer and information sciences, Physics - Physics and Society, Physics - Data Analysis, Statistics and Probability, FOS: Physical sciences, Computer Science - Social and Information Networks, Physics and Society (physics.soc-ph), Data Analysis, Statistics and Probability (physics.data-an)
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