Precise Calculation of a Bond Percolation Transition and Survival Rates of Nodes in a Complex Network
Through precise numerical analysis, we reveal a new type of universal loopless percolation transition in randomly removed complex networks. As an example of a real-world network, we apply our analysis to a business relationship network consisting of approximately 3,000,000 links among 300,000 firms and observe the transition with critical exponents close to the mean-field values taking into account the finite size effect. We focus on the largest cluster at the critical point and introduce survival probability as a new measure characterizing the robustness of each node. We also discuss the relation between survival probability and k-shell decomposition.
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Tokyo Institute of Technology
Hirokazu Kawamoto, Hideki Takayasu, Henrik, Jeldtoft Jensen, and Misako Takayasu