Research On Stochastic Model Construction And Analysis Methods Of Multi-type Complex Networks

Complex network stochastic model describes a network model that matches some specific characteristics of the real-world network,and other characteristics are completely randomized.Based on statistical inference,the complex network stochastic model as a reference system can quantify the complicated structural characteristics that are difficult to explain intuitively in the real-world network.In the process of comparison and inference,the stochastic network model helps researchers to deeply understand the inherent laws of the real-world network,and provides a deep scientific knowledge for description and analysis of the complex systems.With the development of complex network research in recent years,the objects in research have become more complex and larger in scale.Simple homogeneous networks with a single type of nodes and edges have been unable to describe large-scale complex systems with multi-type objects and relationships.More complex network structures,such as multiplex networks,edge-based networks,large-scale sparse networks and heterogeneous networks,are needed to perform accurate abstraction and analysis of such systems.The existing research on stochastic models of simple homogeneous networks is not suitable for the analysis of networks with much more complex structures and larger scales.Therefore,in-depth research for the stochastic models of multi-type compelx networks above is needed to support for the analysis and representation of the complex structural characteristics.In order to fill the gaps of stochastic models in the research of multi-type complex networks,and to further solve the challenges of network stochastic model construction due to network sparsity,our dissertation proposes the multiplex network redundant stochastic model,the edge-based stochastic model,the complex sparse stochastic model,the null model of heterogeneous networks,and the heterogeneous sparse stochastic model,covering all types of complex networks.Our work provides effective analysis and representation tools for the multi-type complex networks,and lay the theoretical foundation for establishing a network science system based on a stochastic model.The main innovations and contributions of this dissertation are as follows:1.Due to the difficulty to solve the redundancy and analyze the complex structure of multiplex networks using existing methods,our dissertation the multiplex network redundant stochastic model theory based on node redundancy.The model has the same node redundancy distribution as the original multiplex network.The specific edge probability of the model is given under the theory of Laplace dynamics.This model describes the redundant relationships between nodes in multiplex networks,and provides a general system framework to quantify specific properties in multiplex networks,including the multiplex community structure.2.Regarding the edges in the network as the main research object,edge-based stochastic model is proposed.The model has an arbitrary and random node degree distribution and the same edge degree distribution as the original network,and provides new insights to the analysis for the edge properties research.The edge-based stochastic model provides a unique and effective edge-core analysis framework,which can be used to analyze edges in network science.The model preserves the basic statistical characteristics of the edge structure,and quantities the complex structural features of the edges.The edge-based stochastic model can be effectively used in the study of complex problems with edges,such as link community detection,motif determination.3.Aiming at the challenge of large-scale network sparsity on the construction of the stochastic models,our dissertation proposes a sparse stochastic model of complex networks by network sparse representation,preserveing the dictionary characteristics of the original network.The network sparse representation is used to decompose and reduce the dimension of the network,extracting the atoms in the network.The sparse stochastic model is built through the reconstruction of the null mode of the atoms.The atoms in the sparse stochastic model can be used for network structure analysis,and can solve the problems of multi-type complex networks,including network similarity measurement,network identification and classification,etc.Therefore,from the decomposition,compression,reconstruction and even prediction of the network,our work implements a complete and scientific network sparse stochastic model representation system.4.Our dissertation proposes the null model and the sparse stochastic model of heterogeneous networks.The null model of heterogeneous networks describes both homogeneous relationships and heterogeneous relationship in the heterogeneous network.Our null model provides a general theoretical framework for quantifying the complex properties in heterogeneous networks.Heterogeneous sparse stochastic model is used for the decomposition and dimensionality reduction of heterogeneous networks,and explores the heterogeneous atoms.A large number of redundant structures in the heterogeneous network are simplified by heterogeneous atoms.Therefore,heterogeneous atoms and their sparse coding are linear representations of heterogeneous networks,and naturally reduce the dimensions of the heterogeneous networks,achieving compression storage of the heterogeneous networks.