Research On Community Detection Methods Of Complex Networks And Its Application In Stock Networks

Complex networks are abstract representations of complex systems.Using complex networks we can analyze the relationships among individuals and the overall structure of complex systems.From the analysis of small graphs to the processing of large-scale networks,the study of complex networks,as a new cross-cutting research field,has attracted the attention of scholars in many fields.Community structure generally exists in many types of complex networks.Exploring the community structure of complex networks helps us to understand various phenomena in the networks.Effective analysis of community structure can significantly improve the performance of complex systems.Based on the analysis of related works,we start from the perspective of network topology structure,and study the static network community detection,dynamic network community detection and the application of community detection in stock networks.The main research contents and contributions are as follows:Firstly,two community detection algorithms for static networks based on quantum evolution are proposed.Modularity is one of widely used standard to measure the quality of community division.If modularity is regarded as an objective function,the problem of community detection can be transformed into an optimization problem.In this thesis,quantum-inspired evolutionary algorithm is introduced into community detection,and probability amplitude encoding of quantum bit is used.Quantum chromosome is used to represent a possible community division in a static network.A new community division is generated by measuring the probability amplitude of quantum bits and collapsing.The community structure corresponding to the optimal modularity is searched in the process of evolution.In order to solve the problem of low convergence rate caused by the increase of network scale,based on the previous algorithm,a guide quantum chromosome is innovatively introduced into the algorithm.It guides the evolution of the whole population in the iterative process and searches for better community division while accelerating convergence.Two algorithms proposed in this thesis can automatically determine the number of communities and effectively discover the community structure in the process of optimization.Secondly,a static community detection algorithm based on extended density peaks-based clustering is proposed.In real complex networks,there are often significant differences in community scale,which will lead to resolution limitation in community division.Therefore,the definitions of connection strength and relative connection coefficient are proposed respectively.Connection strength is used to describe the closeness between nodes,and relative connection coefficient is used to describe the local density of nodes.The definitions of connection strength and relative connection coefficient fully consider similarity of nodes,edge between nodes,degree of nodes and the comparison of connection strength between nodes and their neighbors.Central node in a compact small community can also have a relatively prominent relative connection coefficient,which is easier to be found.After selecting candidate central nodes based on density peaks-based clustering,we further analyze connection strength between candidate central nodes,remove some candidate central nodes with high connection strength,and assign non-central nodes to communities based on connection strength with neighbor nodes.Experiments of benchmark networks and real networks show the number and structure of community detected by our method are closer to real situation.Thirdly,a dynamic network community detection algorithm based on connection strength and evolutionary clustering framework is proposed.In dynamic networks,many community detection algorithms based on evolutionary clustering framework are faced with the problem of selecting balance factor.Under the premise of time smoothness,the value of balance factor can reflect the degree of correlation between the community division of the current time slice and the previous time slice.However,most existing detection algorithms determine this parameter based on experience or experimental results,which ignores the effective information implied by the change of network topology.To solve this problem,we innovatively introduce connection strength into the evolutionary clustering framework.From the perspective of community structure,we transform the cost function into the change of connection strength matrix between nodes,which is expressed as the linear combination of connection strength matrix in adjacent time slices.According to the change range of connection strength matrix between adjacent time slices,balance factor is changed dynamically,and connection strength matrix of the current time slice is modified.On this basis,spectral method is used for division.Finally,the proposed community detection methods are applied to stock networks division and portfolio analysis.In the financial field,the diversification of investment can reduce investment risk,but how to choose a reasonable portfolio is an important problem faced by investors.Therefore,we apply the proposed community detection algorithms to stock networks analysis and use Pearson correlation coefficient to express the correlation between stocks.We construct two types of stock networks: medium and long-term stock networks and short-term stock networks.In the former,the investment portfolio is determined by the results of community division and the topology of the network,and the direction of the investment portfolio is grasped from the overall perspective.In the latter,we can analyze the network of each cycle,detect the network fluctuation in time,and adjust the portfolio flexibly.Based on the Shanghai Stock Exchange 50 stock networks,we have made empirically analysis,which proves the effectiveness of community detection in investment strategy and stock market industry supervision.