Research On Complex Network Structure Characteristics And Its Robustness

With the advent of big data and the Internet era,the scale of complex system in life has gradually expanded.In complex systems,information is often lost due to various accidents.The nature of a network that retains its original working capacity after a part of the lost information is called the robustness of a complex network.In the process of complex network robustness analysis,it is necessary to consider the overall structure of the network and the centrality of each node in the network.The structural characteristics and node centrality of complex networks are widely used in computer science,biology and economics.When studying the robustness of complex networks,reverse thinking is usually used to conduct research.For example,we usually look for relatively good node centrality sequences and delete nodes in the network through the central sequence of nodes(good node centrality).The good sequence can cause the network to crash when a few nodes are lost,by which we can to determine the quality of the node's central sequence,and hence to determine which nodes are more important in a complex network.Finding such a node for protection can improve the robustness of the network.Important nodes in a complex network play an important role in network synchronization,disease propagation,traffic navigation,and cascading failures.In this paper,firstly the evolution process of the network is studied.The diameter of the largest connected subgraph and the average path length of the largest connected subgraph are taken as the criteria to measure the robustness of the network.The robustness of the neutral network,the assortative and the disassortative network with the same degree distribution and different clustering coefficients are comprehensively analyzed.Then combining with the knowledge of graph entropy,a new algorithm called betweenness and degree entropy(BE)is proposed,also subgraph information entropy centrality(SN)and H information entropy centrality(NS)algorithms are proposed based on von Neumann entropy.Betweenness and degree entropy(BE)reflects the correlation between the node itself and its neighbors,and evaluates the impact of Betweenness and degree entropy Centrality on network robustness by static attack and dynamic attack.The simulation results show that BE algorithm has higher attack efficiency than traditional attack strategy in most networks,and is also cond-ucive to identifying the importance of nodes in the network.Subgraph information entropy(SN)and H information entropy(NS)reflect the correlationship between nodes' multi-order neighbors.The influence value R of nodes on propagation dynamics is calculated by SIR model,and then the centrality sequence is determined by Kendall r coefficient.The experimental results show that the new centrality sequence based on graph entropy and von Neumann entropy in this paper is better than traditional central index.The main achievements of this paper are as follows:(1)The influence of clustering coefficient index on the network with the same degree distribution is analyzed.In the experiment,the network maximum connected subgraph diameter and the network average path length are used as indicators to measure the robustness of the network.The results show that the larger the clustering coefficient is,the worse the robustness of the network is.And the clustering coefficient has different effects in different networks.In the disassortative network,the clustering coefficient has a significant effect on the robustness of the network,general impact on neutral networks,and the least impact in assortative network.(2)Betweenness and degree entropy centrality and other classical graph entropy centrality indicators on the robustness of complex networks is analyzed.The relative size of the network's largest connected subgraphs is used as an indicator to measure the robustness of the network.The experimental results show that the central index BE proposed in this paper can quickly reduce the relative size of the largest connected subgraph of the network,and can identify the importance of network nodes well.(3)Using the von Neumann entropy and combining the subgraph centrality and the super H index centrality,two new central indicators,subgraph information entropy(SN)and H information entropy(NS),are proposed.The influence of two new indices on network robustness when network nodes are lost is analyzed.The relative superiority of center sequence is determined by calculating Kendall coefficient ?(Kendall coefficient ? is used to calculate the correlation between sequence R and sequence C,where sequence R represents the influence value of each node in SIR standard model and C represents the center sequence of nodes in network).Experiments show that subgraph information entropy(SN)and H information entropy(NS)perform well in most networks.