title: Precise calculation of a bond percolation transition and survival rates of nodes in a complex network.
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 k-shell decomposition.
authors.affiliation: Department of Computational Intelligence and Systems Science, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, Midori-ku, Yokohama, Japan.
authors.forename: Hirokazu
authors.initials: H
authors.lastname: Kawamoto
authors.affiliation: Department of Computational Intelligence and Systems Science, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, Midori-ku, Yokohama, Japan; Sony Computer Science Laboratories, Shinagawa-ku, Tokyo, Japan; Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, Nakano-ku, Tokyo, Japan.
authors.forename: Hideki
authors.initials: H
authors.lastname: Takayasu
authors.affiliation: Department of Mathematics and Complexity & Networks Group, Imperial College, London, United Kingdom.
authors.forename: Henrik Jeldtoft
authors.initials: HJ
authors.lastname: Jensen
authors.affiliation: Department of Computational Intelligence and Systems Science, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, Midori-ku, Yokohama, Japan.
authors.forename: Misako
authors.initials: M
authors.lastname: Takayasu
mesh_terms: D003132:Commerce / Q000706:statistics & numerical data; D008962:Models, Theoretical; D011336:Probability