Research On Several Kinds Of Entropy And Invulnerability Of Hypernetwork

With the rapid development of social economy,the networking of human society has become a double-edged sword,which not only brings great convenience to human life,but also brings certain negative impacts.If the network is damaged or malfunctioned,it will bring huge losses to human production and life,and seriously affect people's normal life.Therefore,in order to prevent these problems,we need to have a deep understanding of the behavior of various complex networks,and have a deeper understanding of the robustness and invulnerability of the network.However,with the rapid development of human society,complex systems with larger scale,more complex structure and nodes with various attributes have appeared in the real world.In some cases,traditional complex network methods cannot fully and accurately describe the characteristics of complex systems.The hypernetwork based on hypergraph structure provides a new way and method for better understanding and describing more complex real systems.At present,the research on hypernetworks mainly focuses on model construction,topological property analysis(hyperdegree distribution,centrality,clustering coefficient,etc.)and empirical applications,there are few research results on the entropy and invulnerability of hypernetworks.The starting point of this paper is to apply the concept of entropy to the evaluation of the structure and behavioral characteristics of hypernetworks,and based on the hypergraph structure,some basic research work on the entropy and invulnerability characteristics of hypernetworks are carried out.The specific research contents are as follows:1.The definition of three kinds of entropy of hypernetwork is proposed,and the entropy properties of two kinds of hypernetwork are studied and analyzed.Based on hypergraph theory,this paper proposes the definitions of hyperdegree distribution entropy,hyperedge-degree distribution entropy and connected branch entropy,simulates and analyzes the variation of hyperdegree distribution entropy and hyperedge-degree distribution entropy with density in a uniform random hypernetwork,and obtains the corresponding the fitting function.In addition,the theoretical expression of the hyperdegree distribution entropy of the uniform scale-free hypernetwork is obtained through theoretical derivation,and the accuracy of the theoretical analysis is verified by the simulation experiments.At the same time,it is found that compared with the hyperdegree distribution entropy,the hyperedge-degree distribution entropy can better distinguish the uniformity of the hypernetwork.2.The invulnerability of two types of hypernetworks is studied and analyzed from the two measures of node connectivity and hyperedge connectivity.The invulnerability characteristics of hypernetworks under different attack methods and the change of entropy under corresponding values are obtained through simulation.Therefore,from the perspective of entropy,the survivability of the hypernetwork is discussed and analyzed.The results show that entropy has a positive correlation with the invulnerability of hypernetworks,and the invulnerability of random hypernetwork is better than that of scale-free hypernetwork.3.Combined with practical applications,this paper constructs a model of Chinese high-speed rail hypernetwork based on actual data,analyzes the topological properties of the hypernetwork,and combines entropy theory to explore and analyze the invulnerability of the Chinese high-speed rail hypernetwork model based on real data.The results show that the high-speed rail hypernetwork constructed in this paper has scale-free characteristics,and has good invulnerability to random attacks.At the same time,it further verifies the positive correlation between entropy and the invulnerability of hypernetwork.