Abstract:

In a complex network, the damage of core node may affect the stability of the entire network. Therefore, the network invulnerability metric and anti-destructive performance are studied based on the importance of the nodes. Considering the influence of node degree and betweenness on the importance of nodes, a local betweenness-degree centrality index is proposed. Considering the influence of aggregation coefficient on the importance of node invulnerability, the node invulnerability index is proposed, and then the network invulnerability betweenness-degree entropy metric and its algorithm are proposed to measure and evaluate the anti-destructive performance of the whole network. The simulation experiment results show that after about 20% of nodes are removed based on the betweenness-degree centrality attack strategy, the network approximation can be divided into isolated node sets, indicating that the betweenness-degree centrality index is superior to the traditional attack strategy, the importance of nodes can be more accurately portrayed. The calculation results of the invulnerability evaluation of different analog networks show that the ranking of the network’s anti-destructive performance is consistent with the actual situation, and it is completely reasonable in measuring the network invulnerability.

Key words: complex networks, node importance, anti-destructive of network, node centrality

摘要：

在复杂网络中，核心节点的损坏可能会影响到整个网络的稳定性。基于节点重要性研究了网络抗毁性度量和抗毁性能。综合考虑节点度值和介数对节点重要性的影响，提出了局部介-度中心性指标。兼顾节点的聚集系数，提出节点抗毁性度量方法。为了估量网络的抗毁性能，提出了介-度熵度量及其算法。仿真攻击实验结果表明，基于介-度中心性的攻击策略移除约20%的节点后，可将网络近似地分割为孤立节点集合，它优于传统的攻击策略，表明介-度中心性指标可以更准确地刻画节点重要性。对不同模拟网络的抗毁性评估计算结果则表明，介-度熵度量对网络抗毁性能的排序符合实际情况，在衡量网络抗毁性方面是完全合理的。

关键词: 复杂网络, 节点重要性, 网络抗毁性, 节点中心性