Research On Network Reconstruction And Community Detection Based On Dynamics

Many biological,financial,physical,and social systems can be represented by complex networks,so research on complex networks has attracted widespread attention.However,in most cases we do not know the structure of complex systems,so how to infer the network structure based on observation data is an important and challenging inverse problem in network science.In addition,it is also of great significance to perform community detection for a given network,detecting the community structure of a network can analyze the topology and functions of the entire complex network and further discover hidden rules in the network.Based on the above reasons,this dissertation mainly studies the following two issues: network reconstruction and community division.For network reconstruction,inferring the structure and dynamics of complex network systems based on time series data generated by binary dynamics is a challenging problem.The reconstruction methods proposed so far often rely on the knowledge of the dynamics on the networks.In many cases,a prior knowledge of the dynamics is unknown,so it is natural to ask: is it possible to reconstruct network and estimate the dynamical processes on complex networks only rely on the observed data? In this work,we develop a framework to reconstruct the structures of networks with binary-state dynamics,in which the knowledge of the original dynamical processes is unknown.Within the reconstruction framework,the transition probabilities of binary dynamical processes are described by Sigmoid function in logistic regression,we then apply the mean-field approximation to enable maximum likelihood estimation,which gives rise to that the network structure can be inferred by solving the linear system of equations.Meanwhile,the original dynamical processes can be simulated by estimating the parameters in Sigmoid function.Our framework has been validated by a variety of binary dynamical processes on synthetic and empirical networks,indicating that our method can not only reveal the network structures but also estimate the dynamical processes.Moreover,the high accuracy of our method is highlighted by comparing it with the existing methods.We propose improved an attractor algorithm based on distance dynamics to mine community structures.Because the parameters in the original algorithm are sensitively dependent on the size of networks,the types of networks,and so forth,it is hard to provide a uniform value to realize the better community detection.In doing so,we modify the EI term in the original attractor algorithm so that the new EI action no longer contains any parameter.Secondly,in the original algorithm,the peripheral nodes are divided into many isolated communities,leading to the overestimation of community structure.We avoid this problem based on the assumption that the peripheral nodes are classified into the community of neighbor with the largest degree.