Hierarchical Clustering Coarsening Of Complex Networks And Its Application

For all kinds of complex systems in the real world,if we ignore the shape,location and other information of the individual in the system and only consider the relationship between the individual and the individual,we can abstract them into complex networks.Generally,the topological statistical structure of a complex network can be represented by a graph in mathematics,while the dynamic process occurring on the network can be described by a differential dynamic equation.With the development of science and technology,the scale of many real networks is expanding.The huge scale of networks brings great difficulties to the research of complex networks.Many research methods of mesoscale networks are no longer applicable.In order to reduce the complexity of computing time and space,some coarse-grained methods are proposed to reduce the network size while keeping some characteristics of the network.At present,there are some typical coarse-grained methods,such as spectral coarse-grained method,k-kernel decomposition method and so on.In this paper,a new hierarchical clustering based coarse-grained algorithm(HCCG)for complex networks is proposed.Further,the modeling and coarse-grained methods of complex networks are applied to study some characteristics of China's stock market.The main research contents are as follows:(1)A coarsening algorithm(HCCG algorithm)for complex networks based on the clustering method is proposed.Simulation experiments on some typical networks are carried out to verify the effectiveness of this method in keeping the original network synchronization ability in the coarsening process.It is found that the advantages and disadvantages of this algorithm are different under different types of complex networks and different parameters.Using HCCG algorithm to coarse-grained the network can accurately control the size of the coarse-grained network.It is found that this method is more suitable for complex networks with obvious clustering structure.(2)The stock association network is constructed and the HCCG algorithm is used for coarse-grained analysis.The data of stock price is obtained from the trading database of Shanghai and Shenzhen stock market,and the data sequence is preprocessed.The stock data is transformed into symmetric matrix.By setting the threshold value of correlation coefficient,the connection between the stocks with large correlation coefficient is established,and the connection network of unauthorized stock and ticket is constructed.Some topological statistical properties of the network are further studied by applying HCCG coarse-grained algorithm And cluster structure,and analyze the results.