| Complex network is an important tool for analyzing various complex systems.All kinds of complex systems can be transformed into network models for study.The basic components in the system can be transformed into nodes,and the connections or interactions between components can be transformed into edges in the network.With the exploration of complex networks,the research hotspot of complex networks changes from the macrostructure characteristics to the mesostructure and microstructure characteristics.Community structure is a kind of mesoscopic structure characteristic of complex network,which often corresponds to the structural unit of network and functional module of system.By detecting the community structure of complex networks,the corresponding relationship between the structural units of the network and functional modules of the system can be analyzed at the mesoscale level.The centrality measurement of a complex network starts from microscopic individuals and evaluates the relative importance of each node in the network.By evaluating the importance of nodes in the network,the topology and dynamics of the network can be analyzed at the microscale level.Therefore,the research of community structure detection and centrality measurement of complex networks is important topic.The main work of this dissertation is as follows.1.A new similarity measure based on resistance distance of network is proposed and applied to community detection in complex networks.As a measure of the distance between network nodes,the resistance distance can be used as the similarity to analyze the community structure of complex networks.This method calculates the resistance distance between any nodes in the complex networks.Then,the Gaussian kernel function of the resistance distance is used as the weight of the edge in the network.Next,under the constraint of cheeger constant,the weighted network is divided into two subnetworks by bisection spectral method.Finally,repeating this process in the subnetwork,the community structure of the original network can be detected.Furthermore,the proposed method is tested on karate club network,dolphin social network and football club network.The experiment shows the feasibility and effectiveness of this method.2.A new method for detecting community structure is proposed based on the binary relationship and triangle relationship of nodes in complex networks.The triangular structure of the network can reflect the clustering characteristics of network nodes.Therefore,the triangular structure can be used to guide the community structure detection of complex networks.Firstly,the triangular relationship of network is described using 3-uniform hypergraphs.Then,a matrix integrating binary relation and triangular relation is designed,and the community structure of complex network is analyzed by spectral method;Finally,the proposed method has been evaluated on the random network,artificial network and some real-world network.Experimental results show that the proposed method has higher effective and accuracy for discovering the communities.3.The important nodes and network layers of multi-layer complex networks are evaluated based on non-negative tensor factorization.Firstly,the important nodes of single-layer network are evaluated according to nonnegative matrix factorization,and the equivalent relationship between the this method,degree-like centrality measurement and eigenvector centrality measurement is explained.Then,we analyze the limitation and one-sidedness of single-layer complex network model,and introduce the multi-layer complex network model.Finally,based on the nonnegative tensor factorization,a centrality measure is proposed to evaluate the important nodes in multi-layer networks,and the centrality measure is compared with the existing eigenvector centrality measure of multi-layer networks.4.Based on the synchronization of complex networks,the importance of network nodes is evaluated.This centrality measure not only considers the topology of the network,but also considers the synchronization dynamics process of the network.Firstly,the nodes in the network are regarded as oscillators,and all the oscillators of the network are in the same state.Then,every node in the network is disturbed,reveal the importance of the disturbed node through the evolution of the phase difference between the disturbed node and the synchronization state over time.Finally,the centrality measurement is compared with the classical eigenvector centrality measure,and the experimental results show that this method is effective. |
