Effect of variable network clustering on the accuracy of node centrality

Abstract

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.