Generalized theory for node disruption in finite size complex networks

Details Generalized theory for node disruption in finite size complex networks Generalized theory for node disruption in finite size complex networks

2008-11-04

arxiv.org/abs/0811.0513v1

B. Mitra, N. Ganguly, S. Ghose, and F. Peruani, Phys. Rev. E 78, 026115 (2008)

Physics

Data Analysis, Statistics and Probability

Scientific paper

10.1103/PhysRevE.78.026115

After a failure or attack the structure of a complex network changes due to node removal. Here, we show that the degree distribution of the distorted network, under any node disturbances, can be easily computed through a simple formula. Based on this expression, we derive a general condition for the stability of non-correlated finite complex networks under any arbitrary attack. We apply this formalism to derive an expression for the percolation threshold $f_c$ under a general attack of the form $f_k \sim k^{\gamma}$, where $f_k$ stands for the probability of a node of degree $k$ of being removed during the attack. We show that $f_c$ of a finite network of size $N$ exhibits an additive correction which scales as $N^{-1}$ with respect to the classical result for infinite networks.

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