Identification Of Key Nodes Of Complex Networks

The identification of key nodes of complex networks is an important part of complex network theory and complexity science,and identifying the key nodes of complex networks and protecting them in a targeted way can improve the security of the network.At present,the recognition algorithm of key nodes of complex network has some problems,such as inaccurate recognition results and long running time.In order to design an efficient recognition algorithm for key nodes of complex networks,the following studies have been carried out in this paper:(1)Aiming at the method of identifying key nodes by using structural hole theory to pay insufficient attention to the global topology of the network,this paper presents a method for identifying key nodes based on the structure hole theory of Spark GraphX(C-Burt).Firstly,the closeness center index with global characteristics is realized on the Spark GraphX platform,and the calculation time of the closeness center is shortened.Secondly,the closeness center index with global characteristics and adjacency index with local characteristics are combined to improve the formula of network constraint coefficient,and the influence of Node degree attribute and "bridging" attribute on network constraint coefficient is considered comprehensively.Finally,the C-Burt method is implemented on the Spark GraphX distributed graph processing platform,and the validity of the method is evaluated by using the maximum connected sub-graph ratio,the number of sub-diagrams,the network efficiency,the spectral distance and the vulnerability index.(2)Aiming at the problem of long running time when identifying key nodes by using betweenness index,In this paper,an improved betweenness algorithm is proposed to identify key nodes.The graph backtracking-based betweenness algorithm(Brands)is improved,Firstly,the formula for calculating the midpoint degree of node to source node is put forward.Secondly,the information that needs to be recorded when calculating the point degree of the node to the source node is obtained by graph traversal,and its calculation is carried out.Finally,an improved betweenness algorithm is implemented on the Spark GraphX distributed graph processing platform,the betweenness of nodes is calculated,and the key nodes of the network are identified.The validity of the proposed method is verified by experiments.(3)The method of identifying key nodes by multi-indicator not only does not considers the influence of structural hole characteristics on the importance of nodes,but also does not consider the influence of subjective and objective factors on the weight of the indicator,this paper presents an improved method of identifying key nodes using multiple-indicator.Firstly,the importance of nodes is measured by using multiple measurement indicators and structural hole characteristics at the same time.Secondly,the subjective weight of the index is calculated by using the subjective empowerment method,and the objective weight of the index is calculated by using the objective empowerment method.Finally,the subjective weight and objective weight of the index are combined to obtain the comprehensive weight,calculate the importance of the node,and identify the key nodes of the network.The validity of the proposed method to identify the key nodes is verified by experiments.