The Research On Detecting Community Structure Of Complex Networks And Its Application In Financial Networks

As a new emerging discipline, research on complex networks attracts scientists from a variety of different fields. Breakthrough has been made in physics, information science, biology, mathematics, sociology and management science, and sustainable influence is produced on these fields. Complex networks are wheels within wheels on the surface, but most of complex networks have community structure characteristic in essence. It is important to research these properties because they show the global features of complex networks, which assist us to better understand and interpret practical problems that community structure stands for. Detecting community structure is very hard and is not yet satisfactorily solved, despite the huge effort of scientists working on it over the past few years. A widely used measure for evaluating the community structure of complex networks is called modularity (known as Q). It was a very effective method and a kind of methods aiming to maximize the modularity was developed. However the index of Q may fails to identify modules smaller than a scale community.Beginning with the issues related to the definition of community structure, this thesis deals with the indexes of modularity and modularity density, analyzes the undirected and unweighted networks, directed and unweighted networks and directed and weighted networks, defines the standard of communities partition on different types of networks, proposes systematic detection method of community structure. It mainly contains:1. The community structure definition difference is analyzed and compared, based on the standard of definition and pattern of qualitative and quantitative. The easy heuristic algorithm basing on definition of community in a strong sense is constructed. Simulation results demonstrate the validity of the easy heuristic algorithm. This dissertation theoretically analyzes the indexes of modularity Q and modularity density D for community structure measurement. Based on the concepts of intra-cluster density and inter-cluster density, a new community structure index C is proposed. In addition, this dissertation studies the physical meaning of C and analyzes the attribute of C such as boundedness, differentiability, monotonicity and so on. Through the experiment, compare the differences on community partition and the sensitivity of indexes, when the modularity Q, modularity density D, and communicability C are adopted as the optimization objective function respectively.2. Aiming to detect community in the undirected and unweighted networks, the appropriate encoding and decoding method are designed, and the bidirectional crossover method and inferior allele mutation method are constructed. Then the framework of improved genetic optimization algorithm is proposed. The algorithm is applied to Zachary Karate Club Network and College Football Network. Simulation test shows that the proposed approach has a good performance especially comparing with the GN algorithm. At last this dissertation discusses on the experimental results of community partition by selecting the modularity, modularity density and communicability as optimization objective.3. The current studies on community structure mainly manifests in undirected networks, however, few research focus on directed networks. The commonest approach is to detect communities in directed networks by ignoring the edge directions. But such type of approach frequently fails and results in inaccurate community partition because simply discarding edges’ direction is equal to removing valuable information. This dissertation proposes the community structure definition of directed networks based on community structure of undirected networks and characteristic of directed networks. At the same time, the quantitative index of directed connectivity is put forward based on the feature of directed networks connectivity and accessibility. The directed networks model of classical sixteen nodes is used to test the index of directed connectivity, and the experimental results show that the quantitative index of directed connectivity is practicable. This dissertation analyzes the density, strength and connectivity of communities in directed and weighted networks, and mainly analyzes the differences between similitude weighted and dissimilar weighted, between node weighted and edge weighted. The index of weighted communicability is introduced based on connection strength and connection density of weighted community. The detection method of directed weighted networks is put forward, including connection density, connection strength and connectivity. The ring networks model of sixteen nodes is used to examine the change of the index of weighted communicability, and the results show the validity of thw algorithm.4. This dissertation discusses the feasibility of research financial network using complex network theory, constructs the model of financial network, and analyzes statistics characters of this network based on the economic complexity and relation complexity of financial network. Then this paper detects the community structure and analyzes the fund flow in financial network, regarding the financial network as un-weighted and weighted network respectively.