The Node Importance In Temporal Networks Based On Epidemic Spreading

The identifying and ranking of important nodes in temporal networks have attracted much attention for a long time,which can be used to control the spread of disease or information.Research on node importance has wide applications across many disciplines,such as information transmission,viral marketing,network epidemiology,etc.In this paper,we studied the importance of nodes based on Susceptible-Infectious（SI）epidemic spreading model with empirical data from the influence maximization and sentinel surveillance.Firstly,we study the topological structures of three empirical networks and find that for all the networks the density are high and there are a large number of multiple links between nodes.Therefore,we introduce the contact thresholdθto sparse the networks.We find that the topological structures change dramatically whenθ=2.Besides,a new indicator named threshold degree is put forward on the basis of contact threshold,which can effectively identify the active nodes.Secondly,we study the node importance from the aspect of influence maximization.Based on SI spreading model,we first define the spreading ability of each node to measure the node importance.The spreading ability of a source node is calculated from the probability that susceptible nodes are infected by the source.At the same time,we use four metrics,namely temporal degree（TD）,degree（D）,threshold degree（Ts D）and emergence time（ET）to rank the node importance from the perspective of network connectivity.Finally,we analyze the correlation and ranking accuracies of node importance between spreading dynamics and network connectivity..The results show that the threshold degree is a good indicator in ranking node importance since the nodes with higher threshold degree always have higher spreading ability.The temporal degree only works better in the beginning and has less influential than the threshold degree and static degree eventually.Finally,we study the node importance through sentinel surveillance.Sentinel surveillance is to select sentinel nodes carefully according to different strategies,and monitor the infection status of these nodes,in order to report the outbreaks early.To assess the ability to detect epidemic outbreaks early,we define two evaluation parameters:the monitoring time and monitoring efficiency.The simulations on empirical data show that the sentinel strategy depends on topological characteristics,and we further propose two methods to locate sentinels:the second-order broadest neighbor strategy(2^nd LN)and second-order threshold neighbor strategy(2^nd Ts DN).The second-order broadest neighbor strategy means that we randomly select some nodes and set the nodes with largest degrees of their second-order neighbors as sensors.The second-order threshold neighbor strategy means that we set the nodes with largest threshold degrees of their second-order neighbors as sensors.Empirical analysis is performed on six sentinel strategies,we calculate the importance of sentinels by advance time,monitoring timeand monitoring efficiency.The results show that the sentinel selected by the second-order broadest neighbor strategy and the second-order threshold neighbor strategy work best.