Research On Recognition Method Of Key Nodes In Complex Networks Based On Node Centrality

With the advent of the information age and the geometric growth in the volume of network data,complex networks have become a popular research problem in network science.Many mechanisms,such as the spread of epidemics,the proliferation of rumours,the spread of social emergencies and e-commerce advertising,are closely linked to the dynamics of complex networks.Some special nodes greatly affect the structure and function of the network,and can quickly transfer information to more nodes in the network,thus acting to accelerate or control the spread;these nodes are called key nodes.Examples include promoting positive communication and controlling the spread of rumours in social networks,quantifying the scientific results of scientists in collaborative networks,preventing cascading failures in electrical networks and predicting essential proteins in biological networks.Mining critical nodes in complex networks helps to study the structure and characteristics of the network and is extremely important for maintaining the stable operation of the network.By reading a large amount of literature,learning the relevant basic theories in the field of complex networks,and deeply analyzing the shortcomings and inadequacies of existing key node identification algorithms.Combining the current research status and the existing problems,the following two main approaches are proposed:Firstly,a new key node ranking algorithm based on K-shell algorithm and node information entropy is proposed to address the shortcomings of the classical K-shell decomposition algorithm which is too coarse-grained and the problem that the existing algorithm is prone to the phenomenon of "the rich club".The method firstly stratifies the network through the K-shell decomposition algorithm to obtain the Ks value of each node and calculates the information entropy of each node.The concept of comprehensive influence is introduced,and the comprehensive influence of a node is calculated by the Ks value of the node and the information entropy together,which takes into account both the global characteristics of the network and the local attributes of the node,and comprehensively evaluates the importance of the node.In the meantime,by continuously weakening the information entropy of the neighbouring nodes of the selected seed nodes,the seed nodes are more widely and evenly distributed,avoiding the phenomenon of "the rich club".The effectiveness of the method proposed in this thesis is verified through experiments.Secondly,for the study of key node identification in complex networks,it is necessary to consider not only the influence of individual nodes in the network,but also the relationship between the selected nodes influencing each other,by selecting the n nodes in the network that influence each other and have the greatest influence,so that they can be used as the initial propagation nodes,in order to achieve the result of the fastest propagation speed and the widest propagation in the final network,i.e.the most influenced nodes.Based on the study of the heuristic VoteRank algorithm,considering that each node should have a different influence on its different neighbouring nodes and taking into account the influence of low degree nodes,a new key node identification algorithm based on the voting mechanism is proposed.The method first uses the CI algorithm to calculate the CI values of the network nodes,and initialises the voting ability of the nodes by the CI values,fully considering the local information of the nodes as well as the influence of low-degree nodes.At the same time,the concept of voting probability is introduced,through which the voting probability effectively distinguishes the votes of network nodes for their different neighbouring nodes,taking into account more local information and comprehensively assessing the importance of the nodes,and ultimately,the nodes with a larger total number of votes are more important.Experiments demonstrate the superiority of the method proposed in this thesis.