节点中心性对复杂网络传播模式的影响分析

在众多的重要节点评估方法研究中,具有较高中心性的节点一直是关注的焦点,许多传播行为的研究也主要围绕高中心性节点展开,因此在一定程度上忽略了低中心性节点对传播行为的影响.本文从传播异构性角度,通过初始感染最大中心性节点和最小中心性节点揭示网络结构异构性对信息传播的影响.实验结果表明,传播过程中存在"链型"和"扇型"两种传播模式,在初始感染比例不断提升的情况下,两种传播模式的相互转换引发传播速率的变化,进一步促使非线性传播规模交叉现象的产生.这一现象说明,在宏观的信息传播过程中,最小中心性节点的影响力不容忽视,尤其在初始感染比例升高时,最小中心性节点比最大中心性节点更具传播优势.

Analysis of the effect of node centrality on diffusion mode in complex networks

The centrality reflects the importance of a node in a complex network, which plays an important role in the propagation dynamics. Many researches in the field of node ranking estimation have revealed the characteristics of higher centrality in the structural dynamics and propagation dynamics. However, there are few reports about the effect of nodes with a relatively lower centrality on propagation process. In this paper, we focus on the effect of heterogeneous structural characteristics on propagation dynamics. First, we select four centrality measurements (i.e., degree, coreness, betweenness, and eigenvector) and initialize source nodes with the maximum and minimum centralities respectively. Then, based on the email propagation model and the SI model, the massive numbers of elaborate simulations are implemented in twelve scale-free networks. These networks include three networks generated by the Barabási-Albert model, four synthetic networks compiled by the GLP (generalized linear preference) algorithm, and five benchmark networks. The simulation results contain two parts: one is the crossover phenomenon of two propagation processes, and the other is the correlation between the crossover point and the proportion of the initial source nodes. We present the crossover of two propagations by calculating the total infected nodes, the incremental infected nodes, and the average degree of the incremental infected nodes. The average degrees of the incremental infected nodes in both synthetic networks and benchmark networks show that there exist two kinds of diffusion modes (i.e., “fan-shaped” type and “single-strand” type). With the increase of the initial source nodes, the interaction between two modes results in the different dynamic changes of two propagations with respect to propagation speed, which may lead to the crossover of two propagations in terms of propagation scale in the propagation process. Specifically, the increase of the initial source nodes would suppress the propagation process in which nodes with the maximum centralities are portrayed as propagating sources. However, such an effect is not observed in the propagation process in which nodes with the minimum centralities are portrayed as propagating sources. Our further simulation indicates that the crossover points appear earlier as the proportion of the initial source nodes increases. And by employing the discrete-time method, we find that such a phenomenon can be triggered exactly by increasing the initial source nodes. This work reveals that the influence of the nodes with the minimum centralities should be taken into consideration because the initial infected nodes with a lower centrality will lead to a larger propagation scale if the initial proportion is high.