Precise calculation of a bond percolation transition and survival rates of nodes in a complex network

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Abstract

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 relation 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 kshell decomposition.

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Kawamoto, H., Takayasu, H., Jensen, H. J., & Takayasu, M. (2015). Precise calculation of a bond percolation transition and survival rates of nodes in a complex network. PLoS ONE, 10(4). https://doi.org/10.1371/journal.pone.0119979

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