Sasai Takeyuki, Morino Kai, Tanaka Gouhei, Almendral Juan A, Aihara Kazuyuki
Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan.
Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan; Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan; Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan.
PLoS One. 2015 Apr 20;10(4):e0123722. doi: 10.1371/journal.pone.0123722. eCollection 2015.
Understanding network robustness against failures of network units is useful for preventing large-scale breakdowns and damages in real-world networked systems. The tolerance of networked systems whose functions are maintained by collective dynamical behavior of the network units has recently been analyzed in the framework called dynamical robustness of complex networks. The effect of network structure on the dynamical robustness has been examined with various types of network topology, but the role of network assortativity, or degree-degree correlations, is still unclear. Here we study the dynamical robustness of correlated (assortative and disassortative) networks consisting of diffusively coupled oscillators. Numerical analyses for the correlated networks with Poisson and power-law degree distributions show that network assortativity enhances the dynamical robustness of the oscillator networks but the impact of network disassortativity depends on the detailed network connectivity. Furthermore, we theoretically analyze the dynamical robustness of correlated bimodal networks with two-peak degree distributions and show the positive impact of the network assortativity.
了解网络对网络单元故障的鲁棒性，对于防止现实世界网络系统中的大规模故障和损坏非常有用。最近，在复杂网络的动态鲁棒性框架下，分析了由网络单元的集体动态行为维持其功能的网络系统的耐受性。已经通过各种类型的网络拓扑研究了网络结构对动态鲁棒性的影响，但网络 assortativity（度-度相关性）的作用仍不清楚。在这里，我们研究由扩散耦合振荡器组成的相关（ assortative 和 disassortative）网络的动态鲁棒性。对具有泊松和幂律度分布的相关网络的数值分析表明，网络 assortativity 增强了振荡器网络的动态鲁棒性，但网络 disassortativity 的影响取决于详细的网络连通性。此外，我们从理论上分析了具有双峰度分布的相关双峰网络的动态鲁棒性，并展示了网络 assortativity 的积极影响。
