Research On The Measurement Structure Characteristics Of Complex Network Based On Weighted Entropy

In a complex network,there are a large number of nodes and diverse edge connections.The degree distribution of nodes exhibits power law and the network has the characteristics of small world and scale-free.These characteristics are closely related to its topology.At present,many researches on measuring the characteristics of complex network structures based on the degree of nodes are carried out,such as network node importance measurement for network invulnerability analysis and similar nodes identification for community division.However,the directivity of edges and the difference of weights between nodes cause the existing node importance and node similarity to have metric deviation.Therefore,this paper carries out the research on the measurement structure characteristics of complex networks,different models are constructed for complex networks with different characteristics,the concept of weighted entropy is introduced,and two algorithms are designed respectively to conduct the research on the measurement of node similarity and network invulnerability in the topology structure of complex network.The details are as follows:First,in view of the different characteristics of complex networks,two different complex network models are constructed.One is for a real-world complex network that has the relationship between elements through different directions and contains edges with different degrees of association,a degree and strength based directed weighted complex network model is built and a node first-order nearest neighbor local network is defined.These two parts are used for subsequent nodes similarity measurement in directed weighted complex network.The other is for a complex network with two opposite directions and different weights between any two nodes in the network,a dual-direction different-weight edge based complex network model is built and the double-level local network is constructed for each node in the model.These two parts are used to measure the dual-direction different-weight complex network invulnerability.Secondly,for complex connection relationship between nodes and various weights affect the similarity measure of nodes in a complex network with directed weighted edges,a similarity node identify algorithm for directed weighted complex network is designed.The degree and strength based directed weighted complex network model is used to extract multi-index decision probability sets to quantify the structural characteristics of nodes.A Node First-order Nearest Neighbour Local Network Relative Weighted Entropy based Node Similarity Measure is designed to evaluate the influence of the outward&inward degree and strength of nodes in the local network.On this basis,a network similarity node identify algorithm is proposed to measure the similarity between any pair of nodes in a directed weighted complex network and identify the most similar nodes in the network.Thirdly,focusing on the problems about the network invulnerability measurement method is not suitable for complex network with dual-direction different-weight edges,a network invulnerability top nodes mining algorithm for dual-direction different-weight complex network is designed.The constructed dual-direction different-weight edge based complex network model is used to integrate the information of nodes,edges and structures in the local network into the weighted entropy.A Node Double-level Local Structure Weighted Entropy based measure is designed to reveal the influence of the primary-level and the secondary-level of double-level local network.On the basis of the measurement,a network invulnerability top nodes mining algorithm is proposed to mine important nodes that have a greater impact on the network invulnerability.Finally,for the proposed similarity node identify algorithm and network invulnerability top nodes mining algorithm,experiments are designed on different realistic complex networks to verify their effectiveness.The results show that compared with the other three classical methods,the proposed node similarity measurement for complex network can not only mine nodes with the most similarity in the same module,but also mine the most similarity nodes from different modules.At the same time,compared with the other three typical measures,the accuracy of the proposed network invulnerability top nodes mining algorithm is improved by an average of about 28.3%.