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arXiv · 0811.0513

Generalized theory for node disruption in finite size complex networks

Bivas Mitra·Niloy Ganguly·Sujoy Ghose·Fernando Peruani
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Abstract

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 $f_k \sim k^γ$, 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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Bivas Mitra, Niloy Ganguly, Sujoy Ghose, Fernando Peruani. 2008-11-04. Generalized theory for node disruption in finite size complex networks. https://doi.org/10.1103/physreve.78.026115

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