Keywords: 
• 复杂网络 /
• 结构异构性 /
• 中心性 /
• 传播速率

Abstract: 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.