We analyze the betweenness centrality (BC) of nodes in large complex networks. In general, the BC is increasing with connectivity as a power law with an exponent $\eta$. We find that for trees or networks with a small loop density $\eta=2$ while a larger density of loops leads to $\eta<2$. For scale-free networks characterized by an exponent $\gamma$ which describes the connectivity distribution decay, the BC is also distributed according to a power law with a non universal exponent $\delta$. We show that this exponent $\delta$ must satisfy the exact bound $\delta\geq (\gamma+1)/2$. If the scale free network is a tree, then we have the equality $\delta=(\gamma+1)/2$.

Betweenness Centrality in Large Complex Networks

Recently, topology structures of many social, biological and technological networks have been discovered to display a scale-free property. For a network, a community is a natural division of network nodes into groups in which there are more links between nodes within the groups than to nodes outside of it. Many methods of community finding have been proposed to seek a fast, feasible and reasonable partition algorithm for the whole network nodes. In this chapter, we introduce the topology of the network to evaluate the feasibility and correctness of a community finding algorithm. A relationship between the rough number of communities and the magnitude of the number of hub nodes in the network is given in detail firstly. Then, an algorithm based on Laplace matrix spectral decomposition is proposed and its key technology, threshold selection of Euclidean distance between nodes, is discussed. Based on the scale-free topology of complex network, the evaluation criterion of community finding algorithm including three conditions is obtained. Numerical results show that the algorithm of community finding is an effective one and the evaluation criterion is feasible, fast and easy to operate.

Community Finding of Scale-Free Network: Algorithm and Evaluation Criterion

A system of topic mining and dynamic tracking for social texts

According to the research on node centrality of complex network, the existing methods although take the global and local importance of node into account, but don't consider the importance of adjacent edges and the direction of interaction. For this, provides a new method for measuring the node centrality of complex directed network, considers the node's role in network efficiency and degree distribution and the importance of adjacent edges to make the evaluation of node centrality more precisely. An illustrative example proves that the method is reasonable and valid.

Evaluation Method of Node Centrality in Complex Directed Network

With the development of Internet and the sharp increase of the number of netizens, Network is becoming an important public platform for the public to express the opinion, Network public opinion is becoming the improtant base of decision making to the government and companies.Managing the public opinion information and timely discovering hot spots is essential to correctly guiding the public opinion trends, so the Network Public Opinion has become a hot point in this years.Because of the different demand, it is impossible for all the users to acquire the satisfied result.This paper describes an individulized prison Network Public Opinion algorithm based on information network to solve this problem expecially for the judicial authority.

An Individulized Prison Network Public Opinion Algorithm Based on Belief Network

Community finding of virtual user network on the Internet has provoked more and more researchers? interests in the field of computer and physics field recently. Existed results focus on how to seek a reasonable and feasible algorithm to find the communities of virtual user network mostly, but scarcely relate to the centrality of those found communities. In addition, the centrality of those found communities is usually not involved. In this paper, the topology of virtual user network is analyzed firstly, and it shows that the network has a scale-free characteristic. The straightforward and effective criterion evaluating the correctness to detect the community structure has been established. Then the mining system for community finding and centrality of the network is designed and its workflow is presented. Two key modules of this system, community finding module and centrality module, are studied in detail. An implementation example is given to verify the validity of the design. Finally, the paper is summarized.

Mining System for Community Finding and Centrality of Virtual User Network on the Internet

Aiming at the importance of the analysis for public opinion on Internet, the authors propose a high-performance extraction method for public opinion. In this method, the space model for classification is adopted to describe the relationship between words and categories. The combined feature selection method is used to remove noisy words from the original feature space effectively. Then the category weight of words is calculated by the improved formula combining the frequency of words and distribution of words. Finally, the class weights of the not-categorized documents based on the category weight of words are obtained for realizing opinion extraction. Experiment results show that the method has comparatively high classification and good stability.

A high-performance extraction method for public opinion on internet

Data mining of Web hot-topic talks is one of the important branches on the web text mining. In traditional data mining system of the web hot-topic talks, it is assumed that the importance of each web page is equal. However, complex network composed of the web hot-topic talks is not a homogeneous network because of having the scale-free characteristic on the Internet. So the assumption above is not reasonable for this network. In this paper the topology of the complex network is analyzed and shown that the network has the scale-free characteristic firstly. Then the mining system based on the scale-free topology is designed, and some main modules are introduced. The workflow of this system is presented, and the implementations of two core modules, which are the analysis module of sites' topology and the distributing proportion to these web-pages, are proposed in detail. Finally, the merits and shortcomings of this system are concluded, and this paper is summarized.

Guan-zhong Dai

Papers

Mining System for Community Finding and Centrality of Virtual User Network on the Internet

A high-performance extraction method for public opinion on internet

Design and Implementation of Web Hot-Topic Talk Mining Based on Scale-Free Network