Research On The Characteristics Of Topological Structure Of Networks Based On Entropy Theory

The vast majority of real networks are irregular,non-uniform,and extremely complex in structure.The complexity of the network is reflected not only in the heterogeneity of the overall structure,but also in the diversity of the relationship between each node and its neighbors.The structural entropy proposed mainly based on Shannon entropy can characterize the complexity(heterogeneity)of the network,but it also has many shortcomings.For example,when describing the complexity of the network,the traditional structural entropy only focuses on global or local information.In addition,existing studies have shown that although important nodes in a complex network only account for a small part,they can affect the structure and function of the network to a large extent.There are many methods to evaluate node importance in the network,but most methods have the shortcomings of one-sided evaluation angle or too high time complexity.In order to solve the shortcomings of the traditional structural entropy in describing network complexity,this thesis proposes a non-extensive structural entropy of the network based on Tsallis entropy to measure the structural complexity of the network.After comprehensively considering the three characteristic parameters of network nodes,such as degree centrality,betweenness centrality and closeness centrality,the non-extensive entropy parameters of the network are constructed by using integrated centrality and the average values of these three centrality indices respectively.In order to test the performance of this method,real networks and evolutionary model networks are selected for simulation experiments,and theoretical research and simulation experiments are carried out on regular networks,Erd(?)s-Rényi(ER)random networks,Watts-Strogatz(WS)small-world networks and Barabási-Albert(BA)scale-free networks.The results show that the proposed method can well characterize the complexity(heterogeneity)of the network structure,providing a new idea for network design and optimization in reality.This thesis also proposes an evaluation method of network node importance based on local mapping entropy(LME)to balance the effectiveness and efficiency of the evaluation method.The local mapping entropy of a node is mainly divided into two parts: one is the mapping entropy composed of the first-order neighbor nodes of the network node,and the other is the mapping entropy composed of the second-order neighbor nodes of the network node.In order to verify the effectiveness of this method,this thesis uses the invulnerability measure and monotonicity indices under static attack as the evaluation criteria,and compares it with the classical centrality method in real networks and BA and WS standard networks.The experimental results show that the method in this thesis can more effectively and accurately evaluate the importance of network nodes,and at the same time has a high degree of recognition.In addition,the method has low time complexity and can be well applied to large-scale networks.