关键词: 时序网络, 特征向量中心性, 互信息, 联合概率

Abstract: With the vigorous development of various social network platforms, complex network analysis has gradually received extensive attention from researchers in various disciplines. Complex network can be used to describe and research Internet, social network, scientific research cooperation network and paper citation network. Network node importance recognition is an important part of complex network research. It has been widely used in many fields, such as information diffusion mechanism and control, advertising and marketing strategy formulation. The existing methods for identifying the importance of network nodes are mainly based on the global and local structural characteristics of the network, or on the location of nodes in the network, or on the dynamic characteristics of the network. These methods are all based on time independent static networks. Temporal networks carry time information, and their edges appear or disappear over time, which is significantly different from the topology of traditional static networks. Network data not only includes nodes and edges, but also includes contact time information. Therefore, the methods for identifying the importance of nodes in the network are also significantly different from traditional methods.
Temporal network is based on the time window model, which divides the network into multiple time series segments to form a network sequence. The importance measurement of nodes in the network is actually the influence of nodes. From the perspective of information theory, it is the amount of information that nodes transmit to other nodes. In time series network, the amount of information that nodes transmit is different due to the different network structure of each time series window. The existing research calculates the mutual information value between layers from the global perspective through the connected edge probability distribution and the joint probability distribution, and then obtains the overall correlation value between each layer of the network. However, the centrality of nodes in a single network segment cannot reflect the importance of nodes in the entire network sequence. However, the calculation of node importance should reflect the characteristics of nodes in local time and the global changes.
This paper proposes a method to calculate the importance of nodes in temporal networks based on inter layer mutual information. The method first calculates the network eigenvector index in each time window, designs an algorithm model to calculate the correlation between nodes from the probability distribution of node edges in the time series window, calculates the mutual information value of nodes in the layer through the probability distribution of node edges in the time series window and the joint probability distribution of nodes between adjacent windows, and defines the correlation coefficient matrix as the change value of information propagation between nodes in the time window. We take it as the temporal coefficient of each node in each time window, and finally evaluate the importance of each node in the temporal network by combining the feature vector index and the temporal coefficient of the time window.
Finally, the effectiveness of this method in calculating node importance in temporal networks is tested using manufacturing and Enrons real social data. The accuracy of the algorithm is evaluated through the modified SIR model, and the temporal K-kernel decomposition method is compared. The experimental results show that the node importance calculation results of this method had certain advantages compared to other methods. This article only analyzes the changes in node correlation between adjacent time windows, which has certain limitations and loses the information hidden in the whole or multiple time windows. Therefore, how to combine multiple time windows or the whole to measure the changes in node relationships in the network is a problem that needs in-depth research.

Key words: temporal network, centrality of eigenvectors, mutual information, joint probability