网络集聚性对节点中心性指标的准确性影响

节点中心性指标是从特定角度对网络某一方面的结构特点进行刻画的度量指标, 因此网络拓扑结构的改变会对节点中心性指标的准确性产生重要影响. 本文利用Holme-Kim模型构建可变集聚系数的无标度网络, 然后采用Susceptible-Infective-Removal模型进行传播影响力的仿真实验, 接着分析了节点中心性指标在不同集聚系数的无标度网络中的准确性. 结果表明, 度中心性和介数中心性的准确性在低集聚系数的网络中表现更好, 特征向量中心性则在高集聚类网络中更准确, 而紧密度中心性的准确性受网络集聚系数的变化影响较小. 因此当网络的集聚系数较低时, 可选择度或者介数作为中心性指标进行网络节点影响力评价; 反之则选择紧密度指标或特征向量指标较好, 尤其当网络的集聚系数接近0.6时特征向量的准确性可以高达到0.85, 是度量小规模网络的较优选择. 另一方面, 传播过程的感染率越高, 度指标和介数指标越可靠, 紧密度和特征向量则相反. 最后Autonomous System实证网络的断边重连实验, 进一步验证了网络集聚性的改变会对节点中心性指标的准确性产生重要影响.

Effect of variable network clustering on the accuracy of node centrality

Measurements of node centrality are based on characterizing the network topology structure in a certain perspective. Changing the network topology structure would affect the accuracy of the measurements. In this paper, we employ the Holme-Kim model to construct scale-free networks with tunable clustering, and consider the four measurements of classical centrality, including degree centrality, closeness centrality, betweenness centrality and the eigenvector centrality. For comparing the accuracy of the four centrality measurements, we simulate the susceptible-infected-recovered (SIR) spreading of the tunable clustering scale free networks. Experimental results show that the degree centrality and the betweenness centrality are more accurate in networks with lower clustering, while the eigenvector centrality performs well in high clustering networks, and the accuracy of the closeness centrality keeps stable in networks with variable clustering. In addition, the accuracy of the degree centrality and the betweenness centrality are more reliable in the spreading process at the high infectious rates than that of the eigenvector centrality and the closeness centrality. Furthermore, we also use the reconnected autonomous system networks to validate the performance of the four classical centrality measurements with varying cluster. Results show that the accuracy of the degree centrality declines slowly when the clustering of real reconnected networks increases from 0.3 to 0.6, and the accuracy of the closeness centrality has a tiny fluctuation when the clustering of real reconnected networks varies. The betweenness centrality is more accurate in networks with lower clustering, while the eigenvector centrality performs well in high clustering networks, which is the same as in the tunable clustering scale free networks. According to the spreading experiments in the artificial and real networks, we conclude that the network clustering structure affects the accuracy of the node centrality, and suggest that when evaluating the node influence, we can choose the degree centrality in the low clustering networks, while the eigenvector centrality and the closeness centrality are still in the high clustering networks. When considering the spreading dynamics, the accuracy of the eigenvector centrality and the closeness centrality is high, but the accuracy of the degree centrality and the betweenness centrality is more reliable in the spreading process at high infectious rates. This work would be helpful for deeply understanding of the node centrality measurements in complex networks.