Analysis Of Small-world Hypernetwork Model And Spreading Characteristics Based On Hypergraph

With the rapid development of complex systems and complexity science,as an emerging multi-field interdisciplinary subject,network science has attracted extensive attention from experts and scholars in various fields.Small-world characteristics have become one of the research hotspots because they can accurately describe the actual situation of real networks.However,real networks with the characteristics of multi-dimensional,multi-attribute,complexity and large node scale are constantly developing,and the topology and properties of small world networks are also changing,which is difficult to be characterized by traditional complex networks.Therefore,the hypernetwork based on the hypergraph came into being,and the hyperedge in the hypergraph can contain any number of nodes,which can accurately represent various complex and changeable multi-dimensional relationships in real networks.This article comprehensively uses complex networks,hypergraph theory,random process and other related theories,takes hypergraph-based hypernetworks as the main research object,focuses on the small-world hypernetwork model and the spreading dynamics mechanism.The specific research contents are as follows:1.Construction of small world hypernetwork model and study of small world characteristics.Based on the regular hypernetwork,according to the composition of the hyperedges and the different values of the number of hyperedges,two small-world hypernetwork models based on hyperedge random reconnection and hyperedge random addition are proposed and constructed.According to the simulation experiments,the small-world characteristics of the two hypernetwork models are analyzed,and the equivalent random hypernetworks are constructed to verify their small-world characteristics.2.Research on the spreading dynamics of the small-world hypernetworks.In this paper,the small-world hypernetworks are used to describe individual social relationships,combined with the SIR model in spreading dynamics,two information dissemination models on small-world hypernetworks are constructed,and simulation experiments are carried out to analyze the influence of factors such as the structural parameters,transmission parameters,evolution probability of the small-world hypernetwork on the information diffusion speed and steady-state results,revealing the law of information dissemination in social networks from a macro perspective.3.Analyze on the characteristics of empirical hypernetworks.This paper selects real data in typical areas of social networks,infectious disease networks,and cooperative networks,combines hypergraph theory to build different types of empirical hypernetworks,quantitatively analyzes the topological characteristics of the hypernetworks,explores their small-world characteristics and law of information spread,and constructs equivalent random hypernetworks to verify the small-world characteristics of the empirical hypernetworks,analyzes the factors affecting information spread in order to comprehend all kinds of social networks deeply.In summary,the paper first puts forward the core ideas and construction algorithms of the small-world hypernetworks from a theory plane;Secondly,the spreading dynamics models on small-world hypernetworks are constructed to describe the information diffusion law of the real hypernetwork;Finally,empirical studies on real networks are carried out to explore the topology characteristics of networks in different fields.The research in this paper is helpful to provide a certain reference for future research on the small-world characteristics and topological structure of hypernetworks.