Research Of Complex Networks Based On Hypergraph Structure

After the birth of the complex networks science, the end of 20 th century, thousands of researchers who have different academic background have been attracted and millions of achievements have been attained. In the age of 'Big Data', the complex science would bring more influence to people's life and work. As a interdisciplinary,the society need it to produce the benefit rapidly while the physicists and mathematicians persist in find solid theory to support the complex networks science. This thesis aims to introduce hyper graph model into the complex networks, and study the relevant problems from a new perspective.The main contents of this thesis are: 1) Explore a new method to present the complex networks. Hypergraph is introduced in complex network science. And based on hypergraph, real data which has potential multiple relationships could be presented without loss of information. 2) Compare the structure similarities between hypergraph networks and other networks. Through analyzing the scientific networks data which have collaborate relationship and citation relationship,find a similar network(causal law network in cosmological space) in structure property. 3) Establish a new hypergraph network evolution model. Inspired by the idea of casual network of the cosmological space, the hypergraph evolution model, Authority-Similarity-Decline model, is built to present the growth of hyperedges. Hyperbolic geometry and mean-field method are applied to calculate the hyperedge degree distribution function. A simulation experiment is done to compare the simulating results and the real data. And the comparison showed that the distribution function is exact and the ASD-model is appropriate.PNAS(Proceeding of National American Science) data is used to analyzed as a representative of scientific collaborate networks. It is found that the out-degree of the network is linear increase along with the time increase and the size of the networks become larger in exponential growth. It is similar to the universe expansion law. And the causal law is also found in citation network besides in the universe time space. At the same time,PNAS hyperedge degree distribution is also be found that it obeys power law distribution approximately as other kind of complex networks. The ASD-model illustrates the mechanism of hypergraph networks evolution in physics perspective and offers a hand to calculate degree distribution exactly in mathematic perspective. And the simulation of ASD-model shows the trend of degree distribution is similar to that of the real networks.So the model is regarded reasonable.