基于二阶信息的复杂系统弹性度量研究

基于节点最近邻信息，复杂系统弹性预测模型通过将多维方程映射为一维方程，度量复杂系统弹性。然而该模型并未引入节点二阶邻居的信息。基于复杂系统弹性预测模型，通过在映射过程引入节点二阶邻居信息，该文提出了一种考虑节点二阶邻居信息的复杂系统弹性预测模型，并在Barabási-Albert（BA）无标度网络、Watts-Strogatz（WS）小世界网络上验证了新模型的有效性，进而讨论了不同网络拓扑结构对新模型效果的影响。实验结果表明，在平均度不同的BA无标度网络和WS小世界网络中，基于节点二阶邻居信息的复杂系统弹性预测模型均可更准确地预测系统弹性。其中，网络平均度为2的BA无标度网络和WS小世界网络的系统弹性测量精度分别提高了79.89%和59.53%。且在同类网络中，网络平均度越小，基于节点二阶邻居信息的模型越适用。同时，针对同类型平均度相同的网络，改进后模型在BA无标度网络上的效果优于WS小世界网络。该文的研究为有效度量复杂系统弹性状态和设计弹性系统提供了科学的研究手段和理论支持。

Measuring Resilience of Complex Systems via Second-Order Information

Based on the nearest neighbor information of the node, the resilience of complex systems can be measured by using prediction model for complex system resilience through mapping multidimensional equation into one-dimensional equation. However, this model does not introduce the second-order neighbor information of the node. In this paper, we present a prediction model of the resilience of complex systems by considering the second-order neighbor information. Then using the Barabási-Albert (BA) scale free network and Watts-Strogatz (WS) small world network, we investigate the effect of improved model and explore the impact of improved model with different network structures. The experiment results show that for the BA scale free network and WS small-world network with different average degree of network, the improved model considering with the second-order neighbor information can predict the resilience of complex systems more accurately. When the average degrees of the BA scale free network and WS small-world network are 2, the accuracies of system resilience measurement are increased by 79.89% and 59.53%. For the same kind of networks the smaller the average degree of networks is, the more accurate the prediction of the improved model is. Then we also find that when the size and average degree of networks are the same, the effect of improved model is better for BA scale-free network than WS small-word network. Our researches provide theoretical support and research method for measuring resilience of complex networks and designing resilient systems.