How to evaluate the node spreading ability and how to find influential nodes in complex networks are crucial to controlling diseases and rumors, accelerating or hindering information from diffusing, and designing effective advertising strategies for viral marketing, etc. At present, many indicators based on the shortest path, such as closeness centrality, betweenness centrality and the (SP) index have been proposed to evaluate node spreading influence. The shortest path indicates that the information transmission path between nodes always selects the optimal mode. However, information does not know the ideal route from one place to another. The message does not flow only along geodesic paths in most networks, and information transmission path may be any reachable path between nodes. In the network with high clustering coefficient, the local high clustering of the nodes is beneficial to the large-scale dissemination of information. If only the information is transmitted according to the optimal propagation mode, which is the shortest path propagation, the ability to disseminate the node information would be underestimated, and thus the sorting precision of node spreading influence is reduced. By taking into account the transmission rate and the reachable path between a node and its three-step inner neighbors, we design an improved method named ASP to generate ranking list to evaluate the node spreading ability. We make use of the susceptible-infected-recovered (SIR) spreading model with tunable transmission rate to check the effectiveness of the proposed method on six real-world networks and three artificial networks generated by the Lancichinetii-Fortunato-Radicchi (LFR) benchmark model. In the real data sets, the proposed algorithm can achieve a better result than other metrics in a wide range of transmission rate, especially in networks with high clustering coefficients. The experimental results of the three LFR benchmark datasets show that the relative accuracy of ranking result of the ASP index and the SP index changes with the sparseness of the network and the information transmission rate. When the information dissemination rate is small, SP index is slightly better than the ASP index. The reason for this result is that when the transmission rate is small, the node influence is close to the degree. However, when the transmission rate is greater, the accuracy of the ASP index is higher than those of other indicators. This work can shed light on how the local clustering exerts an influence on the node propagation.%评价网络中节点的信息传播影响力对于理解网络结构与网络功能具有重要意义.目前,许多基于最短路径的指标,如接近中心性、介数中心性以及半局部(SP)指标等相继用于评价节点传播影响力.最短路径表示节点间信息传播途径始终选择最优方式,然而实际上网络间的信息传播过程更类似于随机游走,信息的传播途径可以是节点间的任一可达路径,在集聚系数高的网络中,节点的局部高聚簇性有利于信息的有效扩散,若只考虑信息按最优传播方式即最短路径传播,则会低估节点信息传播的能力,从而降低节点影响力的排序精度.综合考虑节点与三步内邻居间的有效可达路径以及信息传播率,提出了一种SP指标的改进算法,即ASP算法.在多个经典的实际网络和人工网络上利用SIR模型对传播过程进行仿真,结果表明ASP指标与度指标、核数指标、接近中心性指标、介数中心性指标以及SP指标相比,可以更精确地对节点传播影响力进行排序.
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