Research On Multi-index Fusion Method Of Recognition Of Vital Nodes In Complex Networks

Complex network is an emergent interdisciplinary,which aims to explain the existence of network phenomena and their complexity.In nature and human society,more and more complex systems can be abstracted into networks,and the simplest form of network can be represented as a set of nodes and a set of edges between connected nodes.Due to the heterogeneity of real networks,nodes play different roles in structure and function,and these nodes which can affect the function of network structure to a greater extent are usually called vital nodes.It is of great significance to identify and utilize the vital nodes in epidemic prevention and control,public opinion guidance,viral marketing and so on.With the increasing of network scale and the complexity of network structure,the importance of evaluating nodes efficiently and accurately has become the focus of scholars.The results of recent researches show that the combinations of multiple indexes can achieve further enhanced ranking results.This paper mainly studies the multi-index fusion method for vital node identification in complex networks.(1)We propose a multi-index fusion method based on D-S evidence theory.Among many indexes for identifying vital nodes,each of them has their own strengths and weaknesses.When faced with different requirements,there is a certain uncertainty in the performance of each index.If these indexes with different emphasis,or even contradictions,can be integrated,the ranking results of vital nodes will be more comprehensive and reliable.To solve this problem,we propose a multi-index fusion method based on D-S evidence theory,which combines the degree of nodes and second-order neighbor information through Dempster rules.The algorithm not only considers the topology information of nodes themselves,but also the topology information of their neighbors,which balances the precision and efficiency well,so it is suitable for large-scale networks.(2)We propose a multi-index fusion method based on information entropy.There are also some problems in the existing multi-index fusion methods.First,the time complexity of these algorithms is higher than O(n),which makes them unsuitable for large-scale networks.Second,these algorithms regard the contribution of each index to the ranking result of vital nodes as equally important,resulting in very limited improvement in algorithm performance.Third,these algorithms select indexes that need to be fused with strong homogeneity in attributes,such as degree,second-order degree,and even third-order degree(these indexes all belong to the neighbor information of nodes).If these indexes are combined,the improvement of algorithms performance will be limited.To solve the above problems,we use information entropy to weight the neighbor information of nodes and the location information in networks,and then conduct fusion.Experimental results show that the proposed algorithm can identify vital nodes efficiently and accurately in large-scale networks.The two multi-index fusion methods proposed in this study further supplement the research system of vital node identification algorithms in complex networks.And because of their low time complexity and high sorting accuracy,they also have high value in practical applications.