The Strucuture, Evolving Models And Spreading Dynamics Of Hypernetworks

In order to analyze the scientific problems behind big data,there is an urgent need to expand the traditional network theory into a new tool.This paper uses the theories of complex networks,hypergraph and hypernetworks,statistical physics,differential equations,stochastic process.Taking social and economic systems as research subjects,the content contains the following topics: topology characterisctics,evolution models and dynamic mechanisms.These three topics interconnect and restrict each other.The reasonable index system is the basis of evaluating the structure of the overall networks.The evolution process can reveal the hidden nature of the network topologies.Meanwhile,the dynamic mechanism drives the evolution of the network,thus results in changing the structure of network.The specific research contents include the following aspects:Firstly,the main topological indices are constructed.Based on the concept of a hypernetwork and the traditional definition of characteristics in complex networks,several new topological characteristics of hypernetworks are defined,namely the strength of the node,the hyperdegree of a hyperedge,the strength of a hyperedge,hyperedge cardinality and so on.Thus the relationships between nodes and hyperedges,among nodes,and among hyperedges can be obtained.Furthermore,the measurement and calculations of structure indicator and cluster coefficient are given.Meanwhile,the collaborative recommendation framework based on hyperedge similarity is also introduced.Quantitative characterizations of complex systems in reality can be depicted by precise mathematical language.It is also the theoretical foundation of the following empirical analysis.Secondly,an empirical study framework of the aforementioned characeristics in conducted.Three real world datasets of cooperative network,competitive network and traffic network are collected,and the construction and statistical analysis are carried out.Different hypernetworks can be constructed where the elements are defined as nodes and the relationships as hyperedges.This involves evaluating the characterisics and law of real hypernetworks at a macro level.Thus this approach may be a good way to deeply understand social networks.The empirical analysis results provide an application basis and realistic support for the construction of evolution mechanism.Thirdly,evolving models driven by different preferential mechanisms and microcosmic events are constructed.According to the structural characteristics presented in real world datasets,several influencing factors on evolution process are abstracted.These theoretical models with different evolutionary rules are constructed to effectively depict the growth of hypernetworks.The paper presents three evolving models driven by hybrid connection mechanism,competitive mechanism and node state conversion mechanism,respectively.In addition,considering the effect of local structure,the paper presents three evolving models driven by neighborhood selection mechanism,interconnection among old nodes and breaking and rewiring of links mechanism.The paper uses Poisson process theory and average field method to obtain the theoretical results.Meanwhile,numerical simulations are carried out to test the impact of different parameters on these models.Finally,the paper compares the actual systems with these theoretical models and then evaluates the effects of these models.Fourth,the propagation dynamics in hypernetworks are studied.The hypernetwork structure is used to depict individual social relationships.Based on the characteristics of information transmission in reality,the transmission modes can be divided into two types: global transmission and local transmission.Based on SIS and SIR epidemic models,the law of information diffusion is studied.The effects of structure parameters,spreading rate,recovering rate and information seed on propagation time and densities of informed nodes are simulated and analyzed.This paper reveals the law of information evolution of social network from a macro perspective.The innovation of the paper is as follows.Firstly,the topological indices of hypernetwork are extended.Combining with the information of the strength of a hyperedge and hyperedge cardinality,the research explores the existing literatures.The specific characteristics can give comprehensive supplement by depicting the relationship between nodes and hyperedges and relationship between hyperedges and hyperedges.Secondly,the empirical research paradigm is given.The paper selects several typical datasets to conduct systematic and in-depth empirical studies,complementing the current theoretical analysis results and the overall law by individual interaction.Thirdly,the evolution models combining with real system characteristics are constructed.The models extend the traditional hypothesis and enrich the existing hypernetwork models.They are used to interprete the empirical data and real systems.Fourth,the information transmission on network is expanded.In reality,individual interacts with multiple neibhbours.The influence of network structure and propagation mode on information spreading is discussed,and the factors associated with the speed and breadth on information spreading are defined.To sum up,the paper firstly gives several topological indices from the theoretical level.Then empirical studies to explore the characteristics of network structure in different fields are conducted from the application level.Finally,the evolutionary dynamic models are constructed to depict the evolution path of real hypernetworks.The paper is helpful to understand the statistical characteristics of real complex systems.