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.
Highlights
Network models have recently garnered considerable attention from physicists because these models are defined out of the Euclidean space and have led to many new insights [11,12,13]
Through precise numerical calculation of a real world example, we prove the existence of percolation transition in complex networks in random removal of links when the network density is very low but non-zero
We analyzed the link-removal percolation transition of a complex business relation network through precise numerical calculation, and concluded that the critical exponents are given by mean-field values
Summary
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. Percolation Transition and Survival Rates in a Complex Network provided support in the form of salaries for authors HT, but did not have any additional role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript. The study of percolation processes in such complex networks is important given the fragility of the systems being modeled [21,22,23,24,25] It is well-known that scale-free networks lose connectivity at high density if nodes are removed in descending order of the degree, showing typical transition behavior [21].
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