Research On Evaluation Algorithms Of Node Importance In Directed-weighted Networks

The relationship between many things in nature can be abstracted as a complex network model.Through the study of the network,you can mine a lot of information hidden behind the network,so as to better serve human society.Due to the heterogeneity of complex networks,there are some special nodes in the network that have a great impact on the structure and function of the network.Once these nodes are attacked,the performance of the network will drop sharply in a short time.Therefore,how to quickly and accurately identify these special nodes is very important.Although researchers have put forward some important node identification algorithms,most of them are for undirected-unweighted networks,these algorithms can not identify the key nodes in the directed-weighted networks.In addition,most networks in the real world need to consider both the direction and the weight of the edge.In order to get close to the real network and identify the key nodes in the network more accurately,it is convenient to solve the real problems effectively.Based on the directed-weighted network,this paper has done the following two works:Firstly,a node importance evaluation algorithm based on entropy method is proposed.This paper uses the degree index to characterize the importance of the node itself,indirectly reflects the importance of the node relative to its neighbors by defining the node attraction rate and node transfer rate,and uses the entropy value method to evaluate the node degree,node attraction rate and node transfer The three indicators of the rate are calculated to obtain the value of the comprehensive evaluation index of node importance.The algorithm not only considers the weight value of the edge between the node and its adjacent point,but also considers the incoming and outgoing strength of its adjacent point,and also considers its own importance and the relative importance of its adjacent point,making the evaluation method more comprehensive.In order to verify the effectiveness of the evaluation algorithm,this paper applies it to symmetric weighted networks and ARPA networks.Experiments show that the algorithm can evaluate the importance of nodes more accurately.In order to further verify the reliability of the proposed algorithm,this paper carried out a cascading failure simulation experiment of static attack and dynamic attack on American aviation network,ARPA network and social network respectively.The experimental results show that when the nodes in the importance list are sequentially removed,the algorithm inthis paper can make the network obtain a smaller maximum connected coefficient and a larger number of subgraphs.Therefore,it shows that the algorithm in this paper is better at identifying key nodes in complex networks.Secondly,a node importance evaluation method based on transfer capability matrix is proposed.Although the evaluation algorithm of node importance based on entropy method has achieved good recognition effect,the importance value is affected to some extent due to the data eliminating negative processing in the process of data dimensionless.In order to avoid this effect and further improve the recognition accuracy,the node contribution capacity matrix and load capacity matrix are defined to reflect the importance of the node relative to its neighbors.Moreover,the node's transmission capacity matrix is calculated based on the contribution capacity matrix and load capacity matrix,and the importance of each node is calculated again through the transmission capacity matrix.Evaluation value,and finally applied the algorithm to American aviation network,neural network,ARPA network and social network.The algorithm also considers the contribution capacity and load capacity of nodes,and improves the accuracy of key node identification.Experiments show that the evaluation method is more effective in distinguishing the differences between nodes in a complex network,and can better identify key nodes.Through the cascading failure experiments,the changes of the maximum connectivity coefficient and the number of subgraphs when the network is subjected to static attacks and dynamic attacks are simulated,which further verifies the reliability of the algorithm.