有限规模复杂网络节点破裂的广义理论
Generalized theory for node disruption in finite size complex networks
摘要：
在故障或攻击之后，复杂网络的结构由于节点移除而改变。在这里，我们证明了在任何节点干扰下，扭曲网络的度分布可以通过一个简单的公式轻松计算。基于这个表达式，我们得到了非相关有限复杂网络在任意攻击下稳定的一般条件。我们应用这种形式主义推导出一个表达式的渗流阈值$f_c$下的一般攻击的形式$f_k \sim k^γ$，其中$f_k$代表的概率节点的程度$k$被删除在攻击。我们发现，$f_c$的大小$N$的有限网络表现出一个附加的校正，其规模为$N^{-1}$相对于经典的结果为无限网络。
英文摘要：
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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