Abstract
The robustness of coupled networks against node failure has been of interest in the past several years, while most of the researches have considered a very strong node-coupling method, i.e., once a node fails, its dependency partner in the other network will fail immediately. However, this scenario cannot cover all the dependency situations in real world, and in most cases, some nodes cannot go so far as to fail due to theirs self-sustaining ability in case of the failures of their dependency partners. In this paper, we use the percolation framework to study the robustness of interdependent networks with weak node-coupling strength across networks analytically and numerically, where the node-coupling strength is controlled by an introduced parameter α. If a node fails, each link of its dependency partner will be removed with a probability 1−α. By tuning the fraction of initial preserved nodes p, we find a rich phase diagram in the plane p−α, with a crossover point at which a first-order percolation transition changes to a second-order percolation transition.
Highlights
Is still lack of study of this mechanism on the robustness of interdependent networks
Our studies show rich phase transition phenomena when the model parameter α changes
We have used the generating function method to solve our model and get the first-order and second-order percolation transition points analytically, which agree with simulation results very well
Summary
Some nodes may disconnect from the largest cluster as a result of the destruction of links in network B The iteration of this process, which alternates between the two networks, leads to a cascade of failures. Let RA be the probability that a randomly chosen link in network A leads to the giant component. − RA)] denotes the giant component of probability that a randomly chosen link network A, and 1 − G0B(1 − RB) is the probability that the dependency partner of this chosen node is still functional. G1A(1 − network αRA)] denotes the probability A leads the giant component of that a randomly chosen network A, and G0B(1 −.
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