The identification of key nodes in complex networks is a hot topic. Therefore, it attracts increasing attention from different fields, like airline networks and social networks. To identify the key nodes in complex network, we suggest an improved gravity model method that takes propagation features into account. Relevant experiments were carried out in four actual airline networks based on the Susceptible Infected Recovered (SIR) model. First, we analyze the correlation between the proposed method and other benchmark methods.Then, Kendall’s correlation coefficient and the imprecision function were used as evaluation metrics to analyze and validate the proposed method. Empirical results reveal that the suggested method outperforms previous benchmark methods in terms of precision and effectiveness for identifying key nodes, especially in the US air network, where Kendall’s tau achieves a 107% improvement compared to the gravity centrality method.

For understanding and controlling spreading in complex networks, identifying the most influential nodes, which can be applied to disease control, viral marketing, air traffic control, and many other fields, is of great importance. By taking the effect of the spreading rate on information entropy into account, we proposed an improved information entropy (IIE) method. Compared to the benchmark methods in the six different empirical networks, the IIE method has been found with a better performance on Kendall’s Tau and imprecision function under the Susceptible Infected Recovered (SIR) model. Especially in the Facebook network, Kendall’s Tau can grow by 120% as compared with the original IE method. And, there is also an equally good performance in the comparative analysis of imprecise functions. The imprecise functions’ value of the IIE method is smaller than the benchmark methods in six networks.

Identifying the key nodes in complicated networks is an essential topic. A number of methods have been developed in recent years to solve this issue more effectively. Multi-attribute ranking is a widely used and efficient method to increase the accuracy of identifying the key nodes. Using k-shell iteration information and propagation threshold differences, we thoroughly analyze the node’s position attribute and the propagation attribute to offer a hybrid influence method based on information entropy. The two attributes will be weighted using the information entropy weighting method, and then the nodes’ influence ranking will be calculated. Correlation experiments in nine different networks were carried out based on the Susceptible–Infected–Recovered (SIR) model. Among these, we use the imprecision function, Kendall’s correlation coefficient, and the complementary cumulative distribution function to validate the suggested method. The experimental results demonstrate that our suggested method outperforms previous node ranking methods in terms of monotonicity, relevance, and accuracy and performs well to achieve a more accurate ranking of nodes in the network.

Information spreading dynamics on the temporal network is a hot topic in the field of network science. In this paper, we propose an information spreading model on an activity-driven temporal network, in which a node is accepting the information dependents on the cumulatively received pieces of information in its recent two steps. With a generalized Markovian approach, we analyzed the information spreading size, and revealed that network temporality might suppress or promote the information spreading, which is determined by the information transmission probability. Besides, the system exists a critical mass, below which the information cannot globally outbreak, and above which the information outbreak size does not change with the initial seed size. Our theory can qualitatively well predict the numerical simulations.

The different rail transit systems, such as regional railway and urban rail transit, cooperate to form the syncretic railway network (SRN). With the rapid development of SRN, the limited transportation capacity is inadequate to meet the booming passenger flow during peak hours, where cascading failures caused by large passenger flow become a threat to SRN. This paper adopts a state equation to depict the failure‐restoration process and investigates detailed restoration strategies considering the characteristics of recoverable and repeatable failures of stations. Specifically, three different restoration strategies—spontaneous restoration strategy (SRS), active restoration strategy (ARS), and hybrid restoration strategy (HRS)—are proposed, and the varying effects of restoration time, restoration probability, restoration objective, and restoration priority for SRN with ARS are compared. These restoration strategies are applied to the actual SRN in Chengdu, where it is found that HRS has a better effect than other strategies. Furthermore, stations in the metro network with higher passenger flow allocate more restoration resources to improve the robustness of SRN, while the restoration effect of SRN increases noticeably with the restoration coefficient and the reserve coefficient. The restoration strategies presented in this paper can improve the safety management of SRN.