Watanabe Shunsuke, Kabashima Yoshiyuki
Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, Yokohama 2268502, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jan;89(1):012808. doi: 10.1103/PhysRevE.89.012808. Epub 2014 Jan 16.
We develop a methodology for analyzing the percolation phenomena of two mutually coupled (interdependent) networks based on the cavity method of statistical mechanics. In particular, we take into account the influence of degree-degree correlations inside and between the networks on the network robustness against targeted (random degree-dependent) attacks and random failures. We show that the developed methodology is reduced to the well-known generating function formalism in the absence of degree-degree correlations. The validity of the developed methodology is confirmed by a comparison with the results of numerical experiments. Our analytical results indicate that the robustness of the interdependent networks depends on both the intranetwork and internetwork degree-degree correlations in a nontrivial way for both cases of random failures and targeted attacks.
我们基于统计力学的腔方法，开发了一种用于分析两个相互耦合（相互依存）网络的渗流现象的方法。特别地，我们考虑了网络内部和网络之间度度相关性对网络抵御有针对性（随机度相关）攻击和随机故障的鲁棒性的影响。我们表明，在不存在度度相关性的情况下，所开发的方法简化为著名的生成函数形式。通过与数值实验结果的比较，证实了所开发方法的有效性。我们的分析结果表明，对于随机故障和有针对性攻击这两种情况，相互依存网络的鲁棒性以一种非平凡的方式依赖于网络内部和网络间的度度相关性。
