Research On The Structure, Modeling And Application Of Complex Hyper - Network

In real world, there are many complex systems which can be described by all kinds of complex networks. Graphs can be used as a unifying tool to describe complex network topologies. Common network-graph is composed of nodes and edges that connect them, which the nodes are used to represent different individuals in the actual system and the edges are used to represent specific relationship between two nodes. With the rapid expansion of the network scale and the more complex connection, there are many large complex networks whose the number of network nodes and edges between nodes are numerous and complex. The general graph sometimes cannot totally characterize its features. Therefore, hypernetworks emerge as the times require. The topological structure of hypernetworks is hypergraph, which the hyperedges in the hypergraph can contain any number of nodes and are used to express the complex multidimensional relationships between nodes. Hypernetworks have been applied in social, biological, ecological and technological systems in the real life.Combining with the hypergraph theory in the thesis, by learning about the model construction and characterization about the complex network, we propose some algorithms of the different hypernetwork models. Then we generate different evolving model for the uniform hypernetworks and random hypernetworks, analyze the properties of the network according to the different hypernetworks model. Therefore, we investigate the application of hypernetworks in the real networks, such as the applications in the scientific collaboration networks and citation networks.The main contents and new results of the thesis are as follows:(1) Constructed the evolving model for the uniform hypernetworksWe constructed three kinds of uniform hypernetworks according to mechanism of the growth of the hyperedges and preferential attachment of the hyperdegree. Then, we proposed three different uniform hypernetwork models, that is, type of (1+m),(m+1) and (l+m), according to the different numbers of new nodes and old nodes which linked to the new ones and formed hyperedges. We analytically studied the hyperdegree distribution of those models and found that those distributions obey a power-law distribution, which the exponents are different and are related to the ratio between the old and the new nodes in the network, i.e., the power exponent increases with the number of new nodes increasing. (2) Constructed the evolving model for the random hypernetworksAs we know, in the real hypernetworks, the number of nodes of the hyperedges is uncertain and randomness. In the thesis, we constructed random hypernetworks model by generating a random number according to the probability. We chosen three different probabilities:uniform probability, probability obeys Poisson distribution and determined probability. And then we constructed those three different random hypernetworks according to those probabilities, thus, we can analysis their hyperdegree distribution by mean-field theory. In conclusion, we found that the hyperdegree distributions obey a power-law distribution and the exponents are different and are related to the different probabilities.(3) Constructed the evolving model for the scientific collaboration networksBased on the hypergraph, by combining with the data of the real-world scientific collaboration network, we constructed a model of hypernetwork. We focused on theoretically analyzing the evolution of published papers, and found that the hyperdegree distribution (the number of published papers) obeys a power-law distribution that the result is consistent with Monte Carlo simulation and analysis of the empirical results. Moreover, the theoretical distribution exponent is γ=1+L/M (L/M is the author growth rate of an evolving scientific networks). Furthermore, by model analysis and empirical test, we found that the exponent y of the hyperdegree distribution was related to authors’growth rate, i.e., the bigger y is, the greater proportion of new authors publishing papers in the field.(4) Constructed the model for citation hypernetworksAccording the data of the real-world citation networks and the evolution of citation networks, we constructed a model of citation hypernetworks. The model not only considered the literature cited times that already existed, but also led an aging into the connection mechanism. We found that the simulation results were consistent with the empirical data. After theoretical analysis, we obtained that the distribution of the article cited times was between scale and exponential distribution. Thus, the early literature showed scale-free features, the recent ones obeyed exponential distribution. Furthermore, by fitting our dynamic model, we found the decay factor of the number of articles have been cited over time was0.75, what’s more, this result is consistent with the calculation in the empirical data sets on the decay factor fitting value.