Research On Vital Node Identification Method Of Hypernetwork Based On Local Characteristics

Complex networks are abstract representations of real complex systems.With the increasing scale of real networks and the increasing complexity of connection modes,complex networks based on ordinary graphs can no longer specifically and effectively portray the multivariate and heterogeneous characteristics of real networks.Hyperedge in the hypernetwork can contain many nodes,making them better able to describe complex real-world systems.Identifying the vital node of the hypernetwork is of great importance to improve the reliability and invulnerability of the hypernetwork,and is conducive to the analysis and study of the functional characteristics and dynamic behavior of the hypernetwork.Vital node identification method based on local characteristics mainly considers the node information and neighbor nodes information.It is suitable for large networks because of its simple operation and low time complexity.Based on the local characteristics,this paper studies the vital node identification methods of the hypernetwork,which mainly include:(1)Vital node identification method of the hypernetwork based on importance measure matrix.The importance of nodes in the hypernetwork depends not only on the influence of nodes themselves and the node efficiency,but also on the contribution of their neighbor nodes.Considering the important of nodes themselves and the influence of neighbor nodes,a new method for identifying vital node of hypernetwork based on importance measure matrix is presented,which is based on the hyper-degree and node efficiency in hypernetwork with the time complexity is(46)(N~2).This method improve the precision of evaluating the importance of the node by integrating the local importance and global importance of the node,so as to meet the actual needs of measuring the importance of nodes.Further,the method is applied to the protein complex hypernetwork,and the results show that the method can effectively mine the vital protein in the protein complex hypernetwork.(2)Vital node identification method of composite index based on local characteristics.Hyper-degree,degree or clustering coefficient indicators are often used to assess the importance of nodes.The hyper-degree index only considers the direct influence of nodes on the hypernetwork.The index only considers the size of neighbor nodes,both ignore the topology information of their neighbor nodes.The clustering coefficient reflects the close relationship between neighbor nodes,but ignores the number of neighbor nodes.In order to break the limitation of single node importance evaluation index,a composite index based on local characteristics is created to evaluate the importance of nodes by using the homotaxis function,combining hyper-degree,degree and clustering coefficient,and then to accurately identify the vital node of the hypernetwork with the time complexity is(46)(N).By sorting out the literature published in the Acta Physica Sinica from 2012 to 2021,this paper constructs a scientific research cooperation hypernetwork and conducts empirical analysis.The results show that this index can effectively identify the vital author in the disciplines.The purpose of this paper is to explore the vital node identification method of the hypernetwork based on local characteristics,and propose a composite index vital node identification method of hypernetwork based on importance measure matrix and local characteristics.Empirical data validation analysis shows that both methods can effectively identify the vital nodes in the corresponding real hypernetworks.This study provides a theoretical basis for further study of hypernetwork dynamic behavior based on hypernetwork topology,and has some reference significance.