中国A股市场股票与其主要投资基金股东组成的二分网性质研究
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摘要
金融系统在国民经济中发挥着越来越重要的作用,股票市场作为金融系统的重要组成部分已经成为为企业融通资金,为投资者提供资本性收入的媒介。中国A股市场从上个世纪九十年代初建立至今,经过了二十年的高速成长,其融资和投资功能已趋向正规和成熟。与西方比较完善的股票市场情况相同,机构投资者在中国A股市场的影响力日渐显现,与A股市场建立之初中小投资者为主的投资格局形成鲜明对比。机构投资者的投资行为对A股市场股票价格的影响越来越受到重视,优秀机构投资者的投资策略也成为众多中小投资者的效仿目标,本文就A股市场中的投资基金和中国A股市场中被投资基金所持有的股票组成的股票-基金二分网进行拓扑结构分析和建模研究,以期发现投资基金的持股行为与整体股票市场指数走势的相关性,以及投资基金每个季度的换股行为特征。
复杂网络理论近年来引起很多学者的关注,并将其应用在众多的研究领域,例如社会网络、互联网、生物网和交通网等等。对复杂网络理论和应用的研究有助于更好的认识网络,识别存在于自然和社会中各种各样实际网络,也有助于研究人员认识网络和揭示实际网络的内在特点和形成规律。复杂网络理论在金融领域的应用主要集中在对全球一些重要股票市场的指数联动性分析和某个股票市场内中众多股票之间价格的相互影响上,或者分析市场内行业板块指数之间的联动性等问题。
股票市场在每天的交易时,产生大量的数据,可以供研究者进行分析。目前,复杂网络理论在研究股东对股票投资的投资行为特征方面的应用研究比较少,股票与股东之间的关系可以用复杂网络理论中的二分网来表示。现实中的许多网络具有二分网的特点,如电影-演员网、科学家-论文网和产品-消费者二分网等等。二分网理论作为复杂网络理论的重要组成部分,已经开始引起众多学者的研究兴趣,二分网的网络拓扑结构可以适用于很多经典单顶点复杂网络难以进行抽象分析的情况中。文献阅读过程中发现,应用复杂网络理论研究股票市场的领域中,很少有对股票与其股东的研究,应用二分网理论对股票和股东组成的二分网的研究刚刚起步,尤其股票-基金二分网的演化模型目前还没有可借鉴的文献发表。因此,本文确定的研究目标设定为中国A股市场中被投资基金持有的股票与其主要的投资基金股东形成的二分网,即“股票-基金”二分网,通过对股票-基金二分网加权投影形成的单顶点股票网和基金网的拓扑结构特征分析和社团结构寻找,提炼出于整体市场走势趋同的要素,再通过股票-基金二分网的静态和动态演化建模仿真过程来验证影响投资基金市场行为的参数和变量。具体来讲,本文的主要研究内容及研究成果如下：
第一,建立“股票-基金”二分网。股票或基金的同类节点之间没有边相连,如果两个基金共同持有几支股票即它们之间存在几条连边,同理,如果两支股票被几个相同的基金所持有则它们之间存在几条连边,以这种加权投影方法分别得到单顶点基金网和单顶点股票网,在对单顶点的股票网和基金网进行统计指标的计算和分析后,本文得出单顶点基金网的小世界特性和无标度特征,但在股票网中只发现其小世界的特性,其度分布并不符合幂率分布,即单顶点股票网不是无标度网络。通过对所选取数据中六个时间点的单顶点基金网和股票网的聚类系数、平均度和平均最短路径变化趋势数据与同一时间节点的上证综合指数相对比,发现它们之间有很强的关联性。
第二,应用二分网的加权投影方法,分别得到单顶点基金网的和股票网,然后对单顶点基金网和股票网应用k-派系社团结构算法进行社团的寻找,找出单顶点基金网和股票网的社团结构。k-派系社团结构方法能够在发现社团结构的同时,找出重叠的节点,重叠的基金节点代表着这些投资基金与其它投资基金持有相同的股票。在分别对单顶点基金网和股票网的社团统计指标值的趋势整理后,我们发现其与同一时期的上证综指的指数变化趋势相一致。
第三,在对“股票-基金”二分网进行演化的建模仿真分析中,本文将其分为静态演化和动态演化两种情况考虑。静态演化假设股票和投资基金的数量不变,即节点数和边数不变；动态演化假设节点数和边数都相应的增加即加点和加边的机制,同时也有节点和边相应的减少即去点和去边的机制。在演化的建模过程中引入局域优先连接机制,与已往的随机选取局域优先连接机制不同,本文将数据中的股票按照行业分类,每个行业作为一个局域来进行内部的优先连接机制建模。在动态演化建模中引入加点、加边、去点、去边和重连五种网络演化的机制。然后分别对静态和动态演化模型中适应度参数和变量进行分析,比较适应度参数及局域内重连概率变量对生成网络结构的影响,还发现在局域优先连接过程中各节点优先概率的选择对仿真结果有很大的影响。在考虑新加入基金节点的适应度参数的随机选取情况对演化结果的影响时,我们发现适应度函数均值中的偏向中间值的数值,会使仿真生成网络的聚类系数、平均度和平均最短路径的变化走势趋向平稳。与实际的网络拓扑结构统计值相比较,仿真模型能够较好的模拟实际的网络演化趋势。
本文将二分网理论运用在投资基金和其所持有股票组成的股票-基金二分网中,与传统的金融学和数学的分析方法相比较,提出了一个新的视角来解释投资基金对股票的投资行为以及与整体市场走势的相关性。对投影后单顶点股票网和基金网的社团结构特征分析,找出其与上证综指走势的趋同性。通过对“股票-基金”二分网的静态演化和动态演化建模仿真,得到了几个对投资基金市场行为的影响具有比较重要意义的参数。
In the national economy, the financial system plays an increasingly important role in financial intermediation for the enterprise, the stock market as an important part of the financial system has become a media to provide investors with capital income. From the early nineties of the last century, China stock market has been undergoing two decades of rapid growth, its financing and investment functions has been getting formal and mature.
In the beginning years of establishment the maim investors of China stock market were individual investors, which was in sharp contrast with mature market in western countries. The influence of institutional investors'behavior in China stock market stock prices has attracted more attention, and many individual investors imitate institutional investors'investment strategy. In this paper, stock selection characteristics of the institutional investors in China stock market in order to find some operation rules.
The stock market produces large amounts of data for researchers to analyze every trading day. At present, the application of complex network theory in the study of shareholder's behavioral characteristics is relatively small, the relationship between the stock and the shareholders can be use showed by bipartite network. In many social networks, such as movie-actor network, scientists-paper network and products consumer bipartite network, show the properties of bipartite network. Recently, complex network theory has attracted the attention of many scholars, and its application in many areas of research, such as social networks, the Internet, biological networks and transport networks. The application of complex networks in the financial sector is mainly concentrated in the linkage analysis of several important stock indexes around the world, or interacting between stocks in the same stock market. Studying the structure of graphs is essential for understanding the structural properties of the application it represents. The study on complex network theory and application can help us to recognize networks, identify the different kinds of practical networks in nature and society; realize networks, find the internal characteristics and evolving rules.
At present, the application of complex network theory in the study of shareholder investment behavior and stock selection characteristics is not enough. The relationship between the stock and the shareholders can be analyzed using complex network theory and this article focuses on the relationship between investment funds shareholders and the stocks in China stock market A:"stock-fund" bipartite network. We use the rule of projecting with weighted edges in order to make fund-network and stock-network, and we explode the community structures of fund-network and stock-network. The generating model is the most important part of this dissertation, and we find that the constructed network model can reflect the actual situation of "stock-fund" bipartite network compared with the actual network. The outline of the paper is as follows.
Firstly, through the simulation analysis we find that in "stock-fund" bipartite network there is no link between two stock nodes or two fund nodes; edges only exist between stock nodes and fund nodes. Since one-mode projection is always less informative than the bipartite representation, we here use a weighting method to better retain the original information. To quantify the weights in the projection network, a straightforward way is adopted to weight an edge directly by the number of times the corresponding partnership repeated. If two fund nodes are shareholders of n stocks, they are considered to have n edges between them."Stock network" and "fund network" are formed and we can obtain the "small world" and "scale free" properties. It is a consequence of the non-uniformity of the connectivity structure, most of the nodes having only a few links and a small number of them having a large number of links. Scale-free property of the stock-network is not found. The clustering coefficient, average degree and average shortest path of the stock-network and fund-network have similar trend with the Shanghai composite index, which can explain our objective of the dissertation.
Secondly, we explode the community structure of the weighted stock-fund bipartite network using the k-clique-communities method. A common feature of complex networks is community structure, the existence of groups of nodes such that nodes within a group are much more connected to each other than to the rest of the network. Communities reflect topological relationships between elements of the underlying system and represent functional entities. Compared with the Shanghai composite index trend, we find that the clustering coefficient, average degree and average shortest path of the stock-network and fund-network show the approximate curves. The structure of community property in fund network may suggest that funds shareholder in one community have same investment perspectives, as they hole the same stock so that they may have similar performance in open market value. This structure is aimed at representing the fact that it is an essential feature of a community that its members can be reached through well connected subsets of nodes. The overlapping community structure of the fund network can explain the institutional investment behavior on some level. Some small funds follow the investment strategy of large-scale funds with good performance. he structure of community property in fund network may suggest that funds shareholder in one community have same investment perspectives, as they hole the same stock so that they may have similar performance in open market value.
By the analysis of the "stock-fund" bipartite network, we propose a model to generate complex bipartite graph without growing and another model to generate the "stock-fund" bipartite network with growing. We classify the stocks according to the profession division standard for stock market and assign the local-world evolving. In these models essential rules are a preferential rewiring process and a fitness function. In the model with growing we put into it all five kinds of rules for generating a bipartite network in order to reflect the actual behavior of the investment funds in the stock market. The fitness parameter plays a important role in the generating model and different initial parameters cause the trend of cluster, average path length and average degree to represent differently with deviations at small values. Considering the parameters of the random selection fitness of new join fund node we find that the median value of fitness function will make the trend of cluster, average path length and average degree smooth. Small value of the average shortest-path length shows that two stock or two investment fund nodes can influence each other easily as the market information spread quickly and investors tend to imitate the behavior of others on some level. Especially, evolving models can not only capture correctly the processes that assembled the networks that we see today, but also help to know how various microscopic processes influence the network topology.
Comparing with the finance and mathematical analysis method, we propose a new perspective to view the institutional investors'behavior in China stock market. The achievements in the paper have significant roles to understand the network topology of "stock-fund" network to build up network models that can simulate the evolving behavior of real networks, and to work out rigorous methods for the statistical properties of networks.
复杂网络理论近年来引起很多学者的关注,并将其应用在众多的研究领域,例如社会网络、互联网、生物网和交通网等等。对复杂网络理论和应用的研究有助于更好的认识网络,识别存在于自然和社会中各种各样实际网络,也有助于研究人员认识网络和揭示实际网络的内在特点和形成规律。复杂网络理论在金融领域的应用主要集中在对全球一些重要股票市场的指数联动性分析和某个股票市场内中众多股票之间价格的相互影响上,或者分析市场内行业板块指数之间的联动性等问题。
股票市场在每天的交易时,产生大量的数据,可以供研究者进行分析。目前,复杂网络理论在研究股东对股票投资的投资行为特征方面的应用研究比较少,股票与股东之间的关系可以用复杂网络理论中的二分网来表示。现实中的许多网络具有二分网的特点,如电影-演员网、科学家-论文网和产品-消费者二分网等等。二分网理论作为复杂网络理论的重要组成部分,已经开始引起众多学者的研究兴趣,二分网的网络拓扑结构可以适用于很多经典单顶点复杂网络难以进行抽象分析的情况中。文献阅读过程中发现,应用复杂网络理论研究股票市场的领域中,很少有对股票与其股东的研究,应用二分网理论对股票和股东组成的二分网的研究刚刚起步,尤其股票-基金二分网的演化模型目前还没有可借鉴的文献发表。因此,本文确定的研究目标设定为中国A股市场中被投资基金持有的股票与其主要的投资基金股东形成的二分网,即“股票-基金”二分网,通过对股票-基金二分网加权投影形成的单顶点股票网和基金网的拓扑结构特征分析和社团结构寻找,提炼出于整体市场走势趋同的要素,再通过股票-基金二分网的静态和动态演化建模仿真过程来验证影响投资基金市场行为的参数和变量。具体来讲,本文的主要研究内容及研究成果如下：
第一,建立“股票-基金”二分网。股票或基金的同类节点之间没有边相连,如果两个基金共同持有几支股票即它们之间存在几条连边,同理,如果两支股票被几个相同的基金所持有则它们之间存在几条连边,以这种加权投影方法分别得到单顶点基金网和单顶点股票网,在对单顶点的股票网和基金网进行统计指标的计算和分析后,本文得出单顶点基金网的小世界特性和无标度特征,但在股票网中只发现其小世界的特性,其度分布并不符合幂率分布,即单顶点股票网不是无标度网络。通过对所选取数据中六个时间点的单顶点基金网和股票网的聚类系数、平均度和平均最短路径变化趋势数据与同一时间节点的上证综合指数相对比,发现它们之间有很强的关联性。
第二,应用二分网的加权投影方法,分别得到单顶点基金网的和股票网,然后对单顶点基金网和股票网应用k-派系社团结构算法进行社团的寻找,找出单顶点基金网和股票网的社团结构。k-派系社团结构方法能够在发现社团结构的同时,找出重叠的节点,重叠的基金节点代表着这些投资基金与其它投资基金持有相同的股票。在分别对单顶点基金网和股票网的社团统计指标值的趋势整理后,我们发现其与同一时期的上证综指的指数变化趋势相一致。
第三,在对“股票-基金”二分网进行演化的建模仿真分析中,本文将其分为静态演化和动态演化两种情况考虑。静态演化假设股票和投资基金的数量不变,即节点数和边数不变；动态演化假设节点数和边数都相应的增加即加点和加边的机制,同时也有节点和边相应的减少即去点和去边的机制。在演化的建模过程中引入局域优先连接机制,与已往的随机选取局域优先连接机制不同,本文将数据中的股票按照行业分类,每个行业作为一个局域来进行内部的优先连接机制建模。在动态演化建模中引入加点、加边、去点、去边和重连五种网络演化的机制。然后分别对静态和动态演化模型中适应度参数和变量进行分析,比较适应度参数及局域内重连概率变量对生成网络结构的影响,还发现在局域优先连接过程中各节点优先概率的选择对仿真结果有很大的影响。在考虑新加入基金节点的适应度参数的随机选取情况对演化结果的影响时,我们发现适应度函数均值中的偏向中间值的数值,会使仿真生成网络的聚类系数、平均度和平均最短路径的变化走势趋向平稳。与实际的网络拓扑结构统计值相比较,仿真模型能够较好的模拟实际的网络演化趋势。
本文将二分网理论运用在投资基金和其所持有股票组成的股票-基金二分网中,与传统的金融学和数学的分析方法相比较,提出了一个新的视角来解释投资基金对股票的投资行为以及与整体市场走势的相关性。对投影后单顶点股票网和基金网的社团结构特征分析,找出其与上证综指走势的趋同性。通过对“股票-基金”二分网的静态演化和动态演化建模仿真,得到了几个对投资基金市场行为的影响具有比较重要意义的参数。
In the national economy, the financial system plays an increasingly important role in financial intermediation for the enterprise, the stock market as an important part of the financial system has become a media to provide investors with capital income. From the early nineties of the last century, China stock market has been undergoing two decades of rapid growth, its financing and investment functions has been getting formal and mature.
In the beginning years of establishment the maim investors of China stock market were individual investors, which was in sharp contrast with mature market in western countries. The influence of institutional investors'behavior in China stock market stock prices has attracted more attention, and many individual investors imitate institutional investors'investment strategy. In this paper, stock selection characteristics of the institutional investors in China stock market in order to find some operation rules.
The stock market produces large amounts of data for researchers to analyze every trading day. At present, the application of complex network theory in the study of shareholder's behavioral characteristics is relatively small, the relationship between the stock and the shareholders can be use showed by bipartite network. In many social networks, such as movie-actor network, scientists-paper network and products consumer bipartite network, show the properties of bipartite network. Recently, complex network theory has attracted the attention of many scholars, and its application in many areas of research, such as social networks, the Internet, biological networks and transport networks. The application of complex networks in the financial sector is mainly concentrated in the linkage analysis of several important stock indexes around the world, or interacting between stocks in the same stock market. Studying the structure of graphs is essential for understanding the structural properties of the application it represents. The study on complex network theory and application can help us to recognize networks, identify the different kinds of practical networks in nature and society; realize networks, find the internal characteristics and evolving rules.
At present, the application of complex network theory in the study of shareholder investment behavior and stock selection characteristics is not enough. The relationship between the stock and the shareholders can be analyzed using complex network theory and this article focuses on the relationship between investment funds shareholders and the stocks in China stock market A:"stock-fund" bipartite network. We use the rule of projecting with weighted edges in order to make fund-network and stock-network, and we explode the community structures of fund-network and stock-network. The generating model is the most important part of this dissertation, and we find that the constructed network model can reflect the actual situation of "stock-fund" bipartite network compared with the actual network. The outline of the paper is as follows.
Firstly, through the simulation analysis we find that in "stock-fund" bipartite network there is no link between two stock nodes or two fund nodes; edges only exist between stock nodes and fund nodes. Since one-mode projection is always less informative than the bipartite representation, we here use a weighting method to better retain the original information. To quantify the weights in the projection network, a straightforward way is adopted to weight an edge directly by the number of times the corresponding partnership repeated. If two fund nodes are shareholders of n stocks, they are considered to have n edges between them."Stock network" and "fund network" are formed and we can obtain the "small world" and "scale free" properties. It is a consequence of the non-uniformity of the connectivity structure, most of the nodes having only a few links and a small number of them having a large number of links. Scale-free property of the stock-network is not found. The clustering coefficient, average degree and average shortest path of the stock-network and fund-network have similar trend with the Shanghai composite index, which can explain our objective of the dissertation.
Secondly, we explode the community structure of the weighted stock-fund bipartite network using the k-clique-communities method. A common feature of complex networks is community structure, the existence of groups of nodes such that nodes within a group are much more connected to each other than to the rest of the network. Communities reflect topological relationships between elements of the underlying system and represent functional entities. Compared with the Shanghai composite index trend, we find that the clustering coefficient, average degree and average shortest path of the stock-network and fund-network show the approximate curves. The structure of community property in fund network may suggest that funds shareholder in one community have same investment perspectives, as they hole the same stock so that they may have similar performance in open market value. This structure is aimed at representing the fact that it is an essential feature of a community that its members can be reached through well connected subsets of nodes. The overlapping community structure of the fund network can explain the institutional investment behavior on some level. Some small funds follow the investment strategy of large-scale funds with good performance. he structure of community property in fund network may suggest that funds shareholder in one community have same investment perspectives, as they hole the same stock so that they may have similar performance in open market value.
By the analysis of the "stock-fund" bipartite network, we propose a model to generate complex bipartite graph without growing and another model to generate the "stock-fund" bipartite network with growing. We classify the stocks according to the profession division standard for stock market and assign the local-world evolving. In these models essential rules are a preferential rewiring process and a fitness function. In the model with growing we put into it all five kinds of rules for generating a bipartite network in order to reflect the actual behavior of the investment funds in the stock market. The fitness parameter plays a important role in the generating model and different initial parameters cause the trend of cluster, average path length and average degree to represent differently with deviations at small values. Considering the parameters of the random selection fitness of new join fund node we find that the median value of fitness function will make the trend of cluster, average path length and average degree smooth. Small value of the average shortest-path length shows that two stock or two investment fund nodes can influence each other easily as the market information spread quickly and investors tend to imitate the behavior of others on some level. Especially, evolving models can not only capture correctly the processes that assembled the networks that we see today, but also help to know how various microscopic processes influence the network topology.
Comparing with the finance and mathematical analysis method, we propose a new perspective to view the institutional investors'behavior in China stock market. The achievements in the paper have significant roles to understand the network topology of "stock-fund" network to build up network models that can simulate the evolving behavior of real networks, and to work out rigorous methods for the statistical properties of networks.
引文
[1]Daniel O. Cajueiro, Benjamin M. Tabak, Filipe K. Werneck. Can We Predict Crashes? Thecase of the Brazilian Stock Market. Physica A,2009,388:1603-1609.
[2]Ding-DingHanetal. Network Topology Affiliated with ASPeeific Airline ComPany, Physica A,388(2009)71-81; Fluctuation of the Download Network, Chinese Phy. Lett, Vol.25No.2(2008)765; Scale-Free Download Network for Publieation, Chinese Phy Lett. Vol.21No.9(2004)1855:A Possible Zpif's, Law in the Nuclear Disassembly, Chinese Science Bulletin,2000; Gravity Model for Transportation Network, Proceedings of the First International Conference on Complex Science:Theory and Applications,2009.
[3]QianJiang-Hai,HanDing-Ding. Gravity Model for Spatial Network Based on Optimal Expected Traffic Act[J]. Physica Sinica58(5),2009,3028-3033.
[4]Ding-Ding Han et al. Fluctuation of the download network. Chinese Phy. Lett. Vol.25No.2,2008,765.
[5]Bianconi G, Barabasi A L, Competition and multiscaling in evolving networks[J]. Europhys. Lett,2001,54:4362442.
[6]方锦清,汪小帆,郑志刚等.一门崭新的交义科学：网络科学(上).物理学进展.2007,Vol.27, No.3:240-343.
[7]王树禾.图论[M],北京：科学出版社,2004：1-5.
[8]Watt D J, Strogatz S H. Collective Dynamics of Small World Networks [J]. Nature,1998, 393(6684):440-442.
[9]Barabasi A L, Albert R. Emergence of Scaling in Random Networks [J]. Science,1999, 286(5439):509-512.
[10]章忠志.复杂网络的演化模型研究：[D].大连：大连理工大学,2006.
[11]Erdos P, Renyi A. On the Evolution of Random Graphs. Publ.Math. Ins. Hun. Acad. Sc., 1960,5:17-60.
[12]Milgram S, The Small World Problem[J]. Psychology Today, May 1967,60-67.
[13]汪小帆,李翔,陈关荣.复杂网络理论及其应用.2005清华大学出版社.
[14]FAN Y, LI M, CHEN J, et al. Network of Econophysicists:a Weighted Network to Investigate the Development of Econophysics [J]. International Journal of Modern Physics B,2004,18:17-19.
[15]LI M, FAN Y, CHEN J, et al. Weighted Networks of Scientific Communication:the Measurement and Topological Role of Weight [J]. Physica A:Statistical Mechanics and its Applications.2005,350(2-4):643-656.
[16]ZHANG P P, CHEN K, HE Y, et al. Model and Empirical Study on Some Collaboration Networks [J]. Physica A:Statistical Mechanics and its Applications,2006,360(2): 599-616.
[17]CHANG H, SU B B, LIU C P, et al. Community, Hierarchy and Interweavement in Collaboration Networks[J]. International Journal of Modern Physics C,2008,19(10): 1537-1554.
[18]官山,何大韧,朱陈平.跨越多个实际科学领域的合作网络与合作-竞争网络[J].力学进展,2008,38-827-834.
[19]HU H, WANG X. Evolution of A Large Online Social Network [J]. Physics Letters A, 2009,373(12-13):1105-1110.
[20]HU H B, WANG X F. Disassortative Mixing in Online Social Networks [J]. Europhysics Letters,2009,86(1):18003.
[21]LI X, JIN Y Y, CHEN G. Complexity and Synchronization of the World Trade Web[J]. Physica A:Statistical Mechanics and its Applications.2003,328(1-2):287-296.
[22]万阳松,陈忠.上海A股市场股价波动相互影响能力实证研究[J].上海管理科学,2006(4)：29-30.
[23]Chen Y Z, Fu C H, Chang H, et al. Connectivity Correlations in Three Topological Spaces of Urban Bus-transport Networks in China [J]. Chin. Phys. B,2008,18: 3580-3587.
[24]Ru W, Xu C. Hierarchical Structure, Disassortativity and Information Measures of the US Flight Network [J]. Chinese Physics Letters,2005,22(10):2715-2718.
[25]Zhang G Q, Zhang G Q, Yang Q F, et al. Evolution of the Internet and Its Cores[J]. New Journal of Physics,2008,10(12):123027 (11pp).
[26]Liu J, Dang Y, Wang Z, et al. Relationship Between the In-degree and Out-degree of WWW [J]. Physica. A,2006,371:861-869.
[27]Portor M E. Competitive Strategy [M]. New York:The Free Press,1995:61272.
[28]Haksnasson. Industrial Yechnological Development:A Network Approach [M]. London, Dover, N.H:Croom Helm,1992.
[29]刘汴生.企业集群网络结构及其绩效研究综述[J].工业技术经济,2007,26(9)：125-128.
[30]郭进利.供应链型网络中双幂律分布模型[J].物理学报,2006,55(8)：3916-392.
[31]朱冰心,胡一竑,基于复杂网络理论的供应链应急管理研究[J].物流技术,第11期,2007.
[32]叶笛,基于复杂网络视角的供应链网络研究[J],现代管理科学,第8期,2011.
[33]胡一竑,朱冰心,复杂网络理论在供应链管理中的应用[J].物流科技,第9期,2007.
[34]Goldberg, D., Nichols D., Oki, B. M., and Terry, D. Using Collaborative Filtering to Weave an Information Tapestry. Comm.(1992), ACM 35,61-70.
[35]T. Hofmann and J. Puzicha. Unsupervised Learning from Dyadic Data. Technical Report TR-98-042, International Computer Science Insitute, Berkeley, CA,1998.
[36]T. Hofmann and J. Puzicha. Statistical Models for Co-occurrence Data. Technical Report AIM-1625, Massachusetts Institute of Technology,1998.
[37]T. Hofmann. Probabilistic latent semantic indexing. In Proceedings of the 22nd Annual ACM Conference on Research and Development in Information Retrieval, page 50, Berkeley, California,1999.
[38]Newman M E J. Scientific Collaboration Networks Construction and Fundamental Results [J]. Physical Review E,2001,64:016131.
[39]Newman M E J. Scientific Collaboration Networks. II. Shortest Paths, Weighted Networks, and Centrality[J]. Physical Review E,2001,64:016132.
[40]傅林华,郭建峰,朱建阳.图书馆图书借阅系统与单标度二元网络模型[J].情报学报,2004,23(5)：571-575.
[41]Guillaume J L, Latapy M, Le-Blond S. Statistical Analysis of a P2P Query Graph Based on Degrees and Their Time-evolution[C]. Das N, Sen A, Das S K, et al. Distributed Computing-IWDC 2004. Berlin:Heidelberg,2005,126-137.
[42]Le Blond S, Guillaume J L, Latapy M. Clustering in P2P Exchanges and Consequences on Performances[C]. Castro M, Renesse R. Peer-to-Peer Systems IV. Berlin:Heidelberg,2005, 193-204.
[43]赫南,淦文燕,李德毅,等.一个小型演员合作网的拓扑性质分析[J].复杂系统与复杂性科学,2006,3(4)：1-10.He Nan, Gan Wenyan, Li Deyi, et al. The Topological Analysis of A Small Actor Collaboration Network [J]. Complex Systems and Complexity Science,2006,3(4):1-10.
[44]刘爱芬,付春花,张增平,等.中国大陆电影网络的实证统计研究[J].复杂系统与复杂性科学,2007,4(3)：10-16.Liu Aifen, Fu Chunhua, Zhang Zengping, et al. An Empirical Statistical Investigation on Chinese Mainland Movie Network[J]. Complex Systems and Complexity Science,2007, 4(3):10-16.
[45]付春花, 刘爱芬等.合作-竞争网络的二分图描述建议[J].数学、力学、物理学、高新技术研究进展,2008(12)：158-163.
[46]王进良,张鹏,狄增如等.北京师范大学图书借阅系统的网络分析[J].情报学报,2009(2),第28卷第1期,137-141.
[47]程婷婷,王恒山,刘建国.用户和项目联合度对二分网络个性化推荐的影响[J].计算机科学,2011(5),38卷第5期：216-219.
[48]陈丽平.加权复杂网络的效率—南京市公共交通网络的实证研究.全国大学生挑战杯竞赛二等奖获奖论文.2005.
[49]赵金山,狄增如,王大辉!北京市公共汽车交通网络几何性质的实证研究[J]复杂系统与复杂性科学,2005,2(2)：45-48.
[50]王炜.城市公共交通系统规划方法与管理技术[M].北京：科学出版社,2002.Wang Wei. Urban Transit Planning and Administration[M]. Beijing:Science Press, 2002.
[51]张译,靳雪翔,张毅.基于二分图的城市公交网络拓扑性质研究[J].系统工程理论与实践.2007(7)：149-155.
[52]M. E. J. Newman. The Structure of Scientific Collaboration Networks[J]. Proc. Natl. Acad. Sci. U.S.A.98,4042001.
[53]A.-L. BarabAsi, H. Jeong, Z. Neda, et al. Evolution of the Social Network of Scientific Collaborations [J]. Physica A 311,2002,590-641.
[54]Latapy M, Magnien C, Vecchio N D. Basic Notions for the Analysis of Large Two-Mode Networks [J]. Social Networks,2006,30:31-48.
[55]Zhou T, Ben J, Medo M, et al. Bipartite Network Projection and Personal Recommendation[J]. Physical Review E,2007,76:046115.
[56]Li M H, Fan Y, Chen J W, et al. Weighted Networks of Scientific Communication:the Measurement and Topological Role of Weight[J]. Physica A,2005,350:643-656.
[57]J. W. Grossman, and P. D. F. Ion. On a Portion of the Well-known Collaboration Graph. Congressus Numerantium,108,129 (1995).
[58]A.-L. Barabasi, et al..Ferromagnetic Phase Transition in Barabasi-Albert Networks[J]. Physica A 311,590,2002:260-266.
[59]J. J. Ramasco, and S. A. Morris. Social Inertia in Collaboration Networks[J]. Phys. Rev. E 73,016122,2006:1-7.
[60]Rosario N. Mantegna. Hierarchical Structure in Financial Markets[J]. Euro. Phys.1999, J. B 11,193-197.
[61]Bonanno G., Lillo F, and Mantegna R.N. High-frequency Cross-correlation in a Set of Stocks[J]. Quantitive Finance.2001, Volume 1,96-104.
[62]N.Vandewalle, F.Brisbois and X.Tordoir. Self-organized Critical Topology of Stock Markets. http://arxiv.org/abs/cond-mat/0009245,2000,1-7.
[63]H.-J. Kim and I.-M. Kim. Scale-Free Network in Stock Markets [J]. Kor Phys Soc,2002,40: 1105-1108.
[64]Giovanni Bonanno, Guido Caldarellil, Fabrizio Lillo et al. Mantegna. Topology of C orrelation Based Minimal Spanning Trees in Real and Model Markets [J]. Phys. Rev. E 68, 046130 (2003).
[65]J.-P. Onnela, K. Kaski and J. Kertesz. Clustering and Information in Correlation Based Financial Networks [J]. Euro. Phys. J. B,2004,38,353-362.
[66]Boginski V, ButenkoS, Panos M. PArdalos. Statistieal Analysis of Financial Networks [J], Computational Statistics & Data Analysis,2005,48:431-443.
[67]Chi K. Tsea, Jing Liua,b, Francis C. M. Laua. A Network Perspective of Stock Market.
[68]黄玮强,庄新田,姚爽.我国股票关联网络拓扑性质与聚类结构分析[J].管理科学,2008,21(3)：94-103.
[69]庄新田,闵志锋,陈师阳.上海证券市场的复杂网络特性分析[J].东北大学学报(自然科学版).第28卷第7期,2007(7),1053-1056.
[70]黄玮强,姚爽,庄新田.上证指数和交易量波动的网络动力学模型[J].东北大学学报(自然科学版),第31卷第10期,2010(10)：1516-1520.
[71]周艳波,蔡世民,周佩玲.金融市场的无标度特征研究[J].中国科技大学学报.第39卷第8期,2009(8)：880-884.
[72]李平,汪秉宏.证券指数的网络动力学模型[J].系统工程.第24卷第3,2006(3)：73-77.
[73]李耀华,姚洪兴.金融危机下股市网络的结构特性研究[J].成都信息工程学院学报.第25卷第1期,2010(2).1.107-111.
[74]李进,马军海.交叉持股行为的复杂性研究[J].北京理工大学学报(社会科学版),第11卷第4期,2009(8).
[75]陈辉煌,高岩.基于复杂网络理论的证券市场网抗毁性分析[J].证券市场.2008(6)：86-89.
[76]G Caldarelli, S Battiston, D Garlaschelli. Emergence of Complexity in Financial Complex Networks [J].2004,650:399-423.
[77]Diego Garlaschelli, Stefano Battiston, Maurizio Castri Vito D. P. et al. The Scale-free Topology of Market Investments [J]. Physica A:Statistical Mechanics and its Applications. 2005,350:491-499.
[78]樊瑛,索丽娜等.复杂网络视角下的NYSE市场投资结构特性研究[J].北京师范大学学报(自然科学版)第44卷第1期,2008(2)：103-105.
[79]陈海阳,张玉林,周长银.基于复杂网络的基金加权网络结构分析[J].佳木斯大学学报(自然科学版).第29卷第1期.2011(1)：36-40.
[80]Kernighan B W, Lin S. A Efficient Heuristic Procedure for Partitioning Graphs [J]. Bell System Technical Journal.1970,49:291-307.
[81]Fiedler M. Algebraic connectivity of graphs. Czech. March. [J].1973,23:298
[82]Pethen A, Simon H, Liou K P. Partitioning Sparse Matrices with Eigenvectors of Graphs. SIAM J.Matrix Anal. Appl,1990,11:430.
[83]汪晓帆,刘亚冰.复杂网络中的社团结构算法综述.电子科技大学学报.2009,第38卷,第5期,537-543.
[84]Girvan M, Newman M E J. Community Structure in Social and Biological Networks[J]. Proc. Narl. Acad. Sci.2001.
[85]Wildinson D, Huberman B A. A Method for Finding Communities of Related Genes[J]. Proc Natl Acad SciUSA,2004,11:5241-5248.
[86]Tyler J, Wilkinson D, Huberman B. Email as Spectroscopy:Automated Discovery of Community Structure within Organizations. International Conference on Communities and Technologies,2003,81-96.
[87]Radicchi F, Castellano C, Cecconi F, Loreto V., Parisi D. Dedining and Identifying Communities in Networks [J]. Proc. Natl. Acad. Sci.,2004,101:2658-2663.
[88]Tsuchiura H, Ogata M, Tanaka Y, Kashiwaya S. Electronic States Around a Vortex Core in High-Tcsuperconductors Based on the T-J model [J]. Phy. Rev. B,2003,68:012509.
[89]Zhou H. Distance, Dissimilarity Index and Network Community Structure [J]. Phys. Rev. E,2003,67:061901.
[90]Fortunato S, Latora V, Marchiori M. A Method to Find Community Structures Based on Information Centrality [J]. Phys. Rev. E,2004,70:056104.
[91]Duch J, Arenas A. Communinty Detection in Complex Networks Using Extreme Optimization. Physical Review E,2005,72:027104.
[92]Danon L, Diaz Guilera A, Duch J, Arenas A. Comparing Community Strctrure Identification [J]. Stat. Mech,2005,09:P09008.
[93]Newman M E J. Fast Algorithm for Detecting Community Structure in Networks. Phys. Rev. E.2004,69:066133.
[94]Clauset A, Newman M E J, Moore C. Finding Community Structure in Very Large Networks [J]. Phys. Rev. E,2004,70:066111.
[95]Donetti L, Munoz M A. Detecting Network Communities:A New Systematic and Efficient Algorithm. Stat. Mech. Theor. Exp.,2004, P10012.
[96]Lancichinetti A, Fortunato S, Kertesz J. Detecting the Overlapping and Hierarchical Community Structure of Complex Networks[J]. New J. Phys.2009,11:033015.
[97]SHEN Hua-wei, CHENG Xue-qi, CAI Kai, et al. Detect Overlapping and Hierarchical Community Structure in Networks [J]. Physica A,2009,388(8):1706-1712.
[98]AHN Y-Y, Bagrow J P, Lehmann S. Communities and Hierarchical Organization of Links in Complex Networks[J/OL]. Eprint arXiv,2009,0903:3178. [2009-03-12]. http://www.arXiv.org.
[99]Palla G, Derrnyi I, Farkas I, et al, Uncovering the Overlapping Community Structure of Complex Networks in Nature and Society [J]. Nature,2005,435:814-818.
[100]Newman M E J, Girvan M. Finding and Evaluating Community Structure in Networks [J]. Phys. Rev. E,2004,69:026113.
[101]Newman M E J, Finding Community Structure in Networks Using the Eigenvectors of Matrices [J]. Physical Review E,2006,74:036104.
[102]Ccndon A, Karp R M. Algorithms for Graph Partitioning on the Planted Partition Model[J]. Random Struct. Algor,2001,18(2):116-140.
[103]Fan Y, LI M, Zhang P, et al. Accuracy and Precision of Methods for Community Identification in Weighted Networks[J]. Physica A,2007,377:363-372.
[104]Lancichinetti A, Fortunato S, Radicchi F. New Benchmark in Community Detection[J/OL]. Eprint arXiv,2008,0805:4770v2. [2009-04-16]. http://www. arXiv.org.
[105]Sawardecker E N, Sales-Pardos M, Amaral L A N. Detection of Node Group Membership in Networks with Group Overlap[J]. Eur Phys J B,2009,67:277.
[106]Dorngovtsev S N, Mendes J F F, Samukhin A N. Structure of Growing Networks with Preferential Linking[J]. Physical Review Letters,2000,85(21):4633-4636.
[107]Dorogovtsev S N, Mendes J F F. Samukhin A N. Size-dependent Degree Distribution of a Scale-free Network[J]. Physical Review E,2001,63(6):062101.
[108]Krapivsky P L, Redner S, Leyvraz F. Connectivity of Growing Random Networks[J]. Physical Review Letters,2000,85:4629-4632.
[109]Amaral L A N, Scala A, Barth618my Met al. Classes of Small-world Networks, Proc. Natl. Acad. Sci. USA,2000,97(21):11149-11152.
[110]Dorogovtscv S N, Mendes J F F. Evolution of Networks with Aging of Sites[J]. Physical Review E,2000,62:1842-1845.
[111]Albert, R., Barabasi, A.L. Topology of Evolving Networks:Local Events and Universaity[J]. Physical Review Letters,2000,85(24):5234-5237.
[112]Dorogovtsev S N, Mendes J. F. F. Scaling Behavior of Developing and Decaying Networks[J]. Europhys. Lett.2000,52:33-39.
[113]Bianconi G, Barabfisi A-L Competition and Multiscaling in Evolving Networks[J]. Europhys. Lett.2001,54:436442.
[114]Erghn G, Rodgers G J. Growing Random Networks with Fitness[J]. Physica A,2002, 303:261.272.
[115]Bianconi G, Barabasi A L. Bose-Einstein Condensation in Complex Networks[J].Phys. Rev. Lett,2001,86:5632-5635.
[116]Li X, Jin Y Y, Chen G. Complexity and Synchronization of the World Trade Web[J]. Physica A,2003,328:287-296.
[117]Li X, Chen G. A Local World Evolving Network Model[J]. Physica A 2003,328: 274-286.
[118]Zhang P, Li M, Mendes J F F, et al. Empirical Analysis and Evolving Model of Bipartite Networks[DR/eL]. [2009-11-13]. http://arxiv. org/abs/0804. 3854vl.
[119]Ferrer R, So16 R V, The Small-world of Human Language[J]. Proceedings of the Royal Society of London B,2001,268:2261-2265.
[120]M. E. J. Newman, S. H. Strogatz, and D. J. Watts. Random Graph Models of Social Networks. Phys. Rev. E 64,026118,2001.
[121]Ohkubo J, Tanaka K, Horiguchi T. Generation of Complex Bipartite Graphs by Using a Preferential Rewiring Process[J]. Physical Review E.2005,72:036120.
[122]O. Pulkkinen and J. Merikoski. Phase Transitions on Markovian Bipartite Graphs-an Application of the Zero-range Process. [J]. Stat. Phys.119,8812005.
[123]张培培,何阅,周涛等.一个描述合作网络顶点度分布的模型.物理学报,55,2006,60-67.
[124]M. Li, D. Wang, Y. Fan, Z. Di, J. Wu. Modelling Weighted Networks Using Connection Count[J]. New J. Phys.8 (2006) 72.
[125]M. Li, J. Wu, D. Wang, T. Zhou, Z. Di, Y. Fan. Evolving Model of Weighted Networks Inspired by Scientific Collaboration Networks[J]. Physica A 375 (2007) 355-364.
[126]潘四军,顾长贵,姜玉梅等.一个客运复合交通网动力学模型?.复杂系统与复杂性科学,5(4),84-88,2008.
[127]B.-B. Su, H. Chang, Y.-Z. Chen, D.-R. He. A Game Theory Model of Urban Public Traffic Networks[J]. Physica A 379,291-297 (2007).
[128]T. Zhou, B.-H. Wang, Y.-D. Jin, et al. Modeling Collaboration Networks Based on Nonlinear Preferential Attachment[J]. Int. J. Mod. Phys. C 18,297-314 (2007).
[129]章忠志,荣莉莉,周涛.一类无标度合作网络的演化模型.系统工程理论与实践.11,57-62,2005.
[130]Evans T S, Plato A D K. Exact Solution for the Time Evolution of Network Rewiring Models[J]. Physical Review E,2007,75:056-101.
[131]H Fan, Wang Z, Ohnishi T, et al. Multicommunity Weight-driven Bipartite Network Model[J]. Physical Review E,2008,78:026103.
[132]Ergun G. Human Sexual Contact Network as a Bipartite Graph[J]. Physica A,2002, 308:483-488.
[133]Guillaume J L, Latapy M. Bipartite Structure of All Complex Networks[J]. Information Processing Letters,2004,90:215-221.
[134]Ramasco J J, DorogovtBev S N, Pastor-Satorras R. Self-organization of Collaboration Networks[J]. Physical Review E,2004,70:036106.
[135]A. Ramezanpour, Europhys. Lett. Biology Helps to Construct Weighted Scale Free Networks.68,316,2004.
[136]Wang D H, Li z, Di z R. Bipartite Producer-Consumer Networks and the Size Distribution of Firms[J]. Physica A,2006,363:359-366.
[137]Lambiotte R, Ausloos M. Uncovering Collective Listening Habits and Music Genres in Bipartite Networks[J]. Physical Review E,2005,72:066107.
[138]Steven A Morris, Gary G Yen. Construction of Bipartite and Unipartite Weighted Networks form Collection of Journal Papers [OL].2006-12-28. http://arxiv.org/PS cache/physics/pdf/0503/0503061v1.pdf
[139]吴亚晶,张鹏,狄增如等.二分网络研究[J].复杂系统与复杂性科学.2010,第7卷第1期：1-12.
[140]Latapy M, Magnien C, Vecchio N D. Basic Notions for the Analysis of Large Two Mode Networks[J]. Social Networks,2008,30:3148.
[141]Li X, Chen, G-R. A Local-World Evolving Network Model [J]. Physica A.2003, 328(1-2):274-286.
[142]Albert R, Barabasi A L. Statistical Mechanics of Complex Networks [J]. Rev. Mod. Phys.,2002,74:47-97.
[143]WATTS D J, STROGATZ S H. Collective Dynamics of Small-Word Networks[J]. Nature,1998,393:440-442.
[144]Newman M E J. The Structure and Function of Complex Networks [J]. SIAM Review, 2003,45(2):167-256.
[145]Latora V, Marchiori M. Economic Small-World Behavior in Weighted Networks [J]. Eur Phys J B,2003,32; 249.
[146]Diego Garlaschelli, Stefano Battiston, Maurizio Castric, et al. Servedio, Guido Aldarelli:the Scale-Free Topology of Market Investments[J]. Physica A,2005,350: 491.
[147]Albert, R., Barabasi, A.L. Topology of Evolving Networks:Local Events and Universality. Physical Review Letters,2000,85(24):5234-5237.
[2]Ding-DingHanetal. Network Topology Affiliated with ASPeeific Airline ComPany, Physica A,388(2009)71-81; Fluctuation of the Download Network, Chinese Phy. Lett, Vol.25No.2(2008)765; Scale-Free Download Network for Publieation, Chinese Phy Lett. Vol.21No.9(2004)1855:A Possible Zpif's, Law in the Nuclear Disassembly, Chinese Science Bulletin,2000; Gravity Model for Transportation Network, Proceedings of the First International Conference on Complex Science:Theory and Applications,2009.
[3]QianJiang-Hai,HanDing-Ding. Gravity Model for Spatial Network Based on Optimal Expected Traffic Act[J]. Physica Sinica58(5),2009,3028-3033.
[4]Ding-Ding Han et al. Fluctuation of the download network. Chinese Phy. Lett. Vol.25No.2,2008,765.
[5]Bianconi G, Barabasi A L, Competition and multiscaling in evolving networks[J]. Europhys. Lett,2001,54:4362442.
[6]方锦清,汪小帆,郑志刚等.一门崭新的交义科学：网络科学(上).物理学进展.2007,Vol.27, No.3:240-343.
[7]王树禾.图论[M],北京：科学出版社,2004：1-5.
[8]Watt D J, Strogatz S H. Collective Dynamics of Small World Networks [J]. Nature,1998, 393(6684):440-442.
[9]Barabasi A L, Albert R. Emergence of Scaling in Random Networks [J]. Science,1999, 286(5439):509-512.
[10]章忠志.复杂网络的演化模型研究：[D].大连：大连理工大学,2006.
[11]Erdos P, Renyi A. On the Evolution of Random Graphs. Publ.Math. Ins. Hun. Acad. Sc., 1960,5:17-60.
[12]Milgram S, The Small World Problem[J]. Psychology Today, May 1967,60-67.
[13]汪小帆,李翔,陈关荣.复杂网络理论及其应用.2005清华大学出版社.
[14]FAN Y, LI M, CHEN J, et al. Network of Econophysicists:a Weighted Network to Investigate the Development of Econophysics [J]. International Journal of Modern Physics B,2004,18:17-19.
[15]LI M, FAN Y, CHEN J, et al. Weighted Networks of Scientific Communication:the Measurement and Topological Role of Weight [J]. Physica A:Statistical Mechanics and its Applications.2005,350(2-4):643-656.
[16]ZHANG P P, CHEN K, HE Y, et al. Model and Empirical Study on Some Collaboration Networks [J]. Physica A:Statistical Mechanics and its Applications,2006,360(2): 599-616.
[17]CHANG H, SU B B, LIU C P, et al. Community, Hierarchy and Interweavement in Collaboration Networks[J]. International Journal of Modern Physics C,2008,19(10): 1537-1554.
[18]官山,何大韧,朱陈平.跨越多个实际科学领域的合作网络与合作-竞争网络[J].力学进展,2008,38-827-834.
[19]HU H, WANG X. Evolution of A Large Online Social Network [J]. Physics Letters A, 2009,373(12-13):1105-1110.
[20]HU H B, WANG X F. Disassortative Mixing in Online Social Networks [J]. Europhysics Letters,2009,86(1):18003.
[21]LI X, JIN Y Y, CHEN G. Complexity and Synchronization of the World Trade Web[J]. Physica A:Statistical Mechanics and its Applications.2003,328(1-2):287-296.
[22]万阳松,陈忠.上海A股市场股价波动相互影响能力实证研究[J].上海管理科学,2006(4)：29-30.
[23]Chen Y Z, Fu C H, Chang H, et al. Connectivity Correlations in Three Topological Spaces of Urban Bus-transport Networks in China [J]. Chin. Phys. B,2008,18: 3580-3587.
[24]Ru W, Xu C. Hierarchical Structure, Disassortativity and Information Measures of the US Flight Network [J]. Chinese Physics Letters,2005,22(10):2715-2718.
[25]Zhang G Q, Zhang G Q, Yang Q F, et al. Evolution of the Internet and Its Cores[J]. New Journal of Physics,2008,10(12):123027 (11pp).
[26]Liu J, Dang Y, Wang Z, et al. Relationship Between the In-degree and Out-degree of WWW [J]. Physica. A,2006,371:861-869.
[27]Portor M E. Competitive Strategy [M]. New York:The Free Press,1995:61272.
[28]Haksnasson. Industrial Yechnological Development:A Network Approach [M]. London, Dover, N.H:Croom Helm,1992.
[29]刘汴生.企业集群网络结构及其绩效研究综述[J].工业技术经济,2007,26(9)：125-128.
[30]郭进利.供应链型网络中双幂律分布模型[J].物理学报,2006,55(8)：3916-392.
[31]朱冰心,胡一竑,基于复杂网络理论的供应链应急管理研究[J].物流技术,第11期,2007.
[32]叶笛,基于复杂网络视角的供应链网络研究[J],现代管理科学,第8期,2011.
[33]胡一竑,朱冰心,复杂网络理论在供应链管理中的应用[J].物流科技,第9期,2007.
[34]Goldberg, D., Nichols D., Oki, B. M., and Terry, D. Using Collaborative Filtering to Weave an Information Tapestry. Comm.(1992), ACM 35,61-70.
[35]T. Hofmann and J. Puzicha. Unsupervised Learning from Dyadic Data. Technical Report TR-98-042, International Computer Science Insitute, Berkeley, CA,1998.
[36]T. Hofmann and J. Puzicha. Statistical Models for Co-occurrence Data. Technical Report AIM-1625, Massachusetts Institute of Technology,1998.
[37]T. Hofmann. Probabilistic latent semantic indexing. In Proceedings of the 22nd Annual ACM Conference on Research and Development in Information Retrieval, page 50, Berkeley, California,1999.
[38]Newman M E J. Scientific Collaboration Networks Construction and Fundamental Results [J]. Physical Review E,2001,64:016131.
[39]Newman M E J. Scientific Collaboration Networks. II. Shortest Paths, Weighted Networks, and Centrality[J]. Physical Review E,2001,64:016132.
[40]傅林华,郭建峰,朱建阳.图书馆图书借阅系统与单标度二元网络模型[J].情报学报,2004,23(5)：571-575.
[41]Guillaume J L, Latapy M, Le-Blond S. Statistical Analysis of a P2P Query Graph Based on Degrees and Their Time-evolution[C]. Das N, Sen A, Das S K, et al. Distributed Computing-IWDC 2004. Berlin:Heidelberg,2005,126-137.
[42]Le Blond S, Guillaume J L, Latapy M. Clustering in P2P Exchanges and Consequences on Performances[C]. Castro M, Renesse R. Peer-to-Peer Systems IV. Berlin:Heidelberg,2005, 193-204.
[43]赫南,淦文燕,李德毅,等.一个小型演员合作网的拓扑性质分析[J].复杂系统与复杂性科学,2006,3(4)：1-10.He Nan, Gan Wenyan, Li Deyi, et al. The Topological Analysis of A Small Actor Collaboration Network [J]. Complex Systems and Complexity Science,2006,3(4):1-10.
[44]刘爱芬,付春花,张增平,等.中国大陆电影网络的实证统计研究[J].复杂系统与复杂性科学,2007,4(3)：10-16.Liu Aifen, Fu Chunhua, Zhang Zengping, et al. An Empirical Statistical Investigation on Chinese Mainland Movie Network[J]. Complex Systems and Complexity Science,2007, 4(3):10-16.
[45]付春花, 刘爱芬等.合作-竞争网络的二分图描述建议[J].数学、力学、物理学、高新技术研究进展,2008(12)：158-163.
[46]王进良,张鹏,狄增如等.北京师范大学图书借阅系统的网络分析[J].情报学报,2009(2),第28卷第1期,137-141.
[47]程婷婷,王恒山,刘建国.用户和项目联合度对二分网络个性化推荐的影响[J].计算机科学,2011(5),38卷第5期：216-219.
[48]陈丽平.加权复杂网络的效率—南京市公共交通网络的实证研究.全国大学生挑战杯竞赛二等奖获奖论文.2005.
[49]赵金山,狄增如,王大辉!北京市公共汽车交通网络几何性质的实证研究[J]复杂系统与复杂性科学,2005,2(2)：45-48.
[50]王炜.城市公共交通系统规划方法与管理技术[M].北京：科学出版社,2002.Wang Wei. Urban Transit Planning and Administration[M]. Beijing:Science Press, 2002.
[51]张译,靳雪翔,张毅.基于二分图的城市公交网络拓扑性质研究[J].系统工程理论与实践.2007(7)：149-155.
[52]M. E. J. Newman. The Structure of Scientific Collaboration Networks[J]. Proc. Natl. Acad. Sci. U.S.A.98,4042001.
[53]A.-L. BarabAsi, H. Jeong, Z. Neda, et al. Evolution of the Social Network of Scientific Collaborations [J]. Physica A 311,2002,590-641.
[54]Latapy M, Magnien C, Vecchio N D. Basic Notions for the Analysis of Large Two-Mode Networks [J]. Social Networks,2006,30:31-48.
[55]Zhou T, Ben J, Medo M, et al. Bipartite Network Projection and Personal Recommendation[J]. Physical Review E,2007,76:046115.
[56]Li M H, Fan Y, Chen J W, et al. Weighted Networks of Scientific Communication:the Measurement and Topological Role of Weight[J]. Physica A,2005,350:643-656.
[57]J. W. Grossman, and P. D. F. Ion. On a Portion of the Well-known Collaboration Graph. Congressus Numerantium,108,129 (1995).
[58]A.-L. Barabasi, et al..Ferromagnetic Phase Transition in Barabasi-Albert Networks[J]. Physica A 311,590,2002:260-266.
[59]J. J. Ramasco, and S. A. Morris. Social Inertia in Collaboration Networks[J]. Phys. Rev. E 73,016122,2006:1-7.
[60]Rosario N. Mantegna. Hierarchical Structure in Financial Markets[J]. Euro. Phys.1999, J. B 11,193-197.
[61]Bonanno G., Lillo F, and Mantegna R.N. High-frequency Cross-correlation in a Set of Stocks[J]. Quantitive Finance.2001, Volume 1,96-104.
[62]N.Vandewalle, F.Brisbois and X.Tordoir. Self-organized Critical Topology of Stock Markets. http://arxiv.org/abs/cond-mat/0009245,2000,1-7.
[63]H.-J. Kim and I.-M. Kim. Scale-Free Network in Stock Markets [J]. Kor Phys Soc,2002,40: 1105-1108.
[64]Giovanni Bonanno, Guido Caldarellil, Fabrizio Lillo et al. Mantegna. Topology of C orrelation Based Minimal Spanning Trees in Real and Model Markets [J]. Phys. Rev. E 68, 046130 (2003).
[65]J.-P. Onnela, K. Kaski and J. Kertesz. Clustering and Information in Correlation Based Financial Networks [J]. Euro. Phys. J. B,2004,38,353-362.
[66]Boginski V, ButenkoS, Panos M. PArdalos. Statistieal Analysis of Financial Networks [J], Computational Statistics & Data Analysis,2005,48:431-443.
[67]Chi K. Tsea, Jing Liua,b, Francis C. M. Laua. A Network Perspective of Stock Market.
[68]黄玮强,庄新田,姚爽.我国股票关联网络拓扑性质与聚类结构分析[J].管理科学,2008,21(3)：94-103.
[69]庄新田,闵志锋,陈师阳.上海证券市场的复杂网络特性分析[J].东北大学学报(自然科学版).第28卷第7期,2007(7),1053-1056.
[70]黄玮强,姚爽,庄新田.上证指数和交易量波动的网络动力学模型[J].东北大学学报(自然科学版),第31卷第10期,2010(10)：1516-1520.
[71]周艳波,蔡世民,周佩玲.金融市场的无标度特征研究[J].中国科技大学学报.第39卷第8期,2009(8)：880-884.
[72]李平,汪秉宏.证券指数的网络动力学模型[J].系统工程.第24卷第3,2006(3)：73-77.
[73]李耀华,姚洪兴.金融危机下股市网络的结构特性研究[J].成都信息工程学院学报.第25卷第1期,2010(2).1.107-111.
[74]李进,马军海.交叉持股行为的复杂性研究[J].北京理工大学学报(社会科学版),第11卷第4期,2009(8).
[75]陈辉煌,高岩.基于复杂网络理论的证券市场网抗毁性分析[J].证券市场.2008(6)：86-89.
[76]G Caldarelli, S Battiston, D Garlaschelli. Emergence of Complexity in Financial Complex Networks [J].2004,650:399-423.
[77]Diego Garlaschelli, Stefano Battiston, Maurizio Castri Vito D. P. et al. The Scale-free Topology of Market Investments [J]. Physica A:Statistical Mechanics and its Applications. 2005,350:491-499.
[78]樊瑛,索丽娜等.复杂网络视角下的NYSE市场投资结构特性研究[J].北京师范大学学报(自然科学版)第44卷第1期,2008(2)：103-105.
[79]陈海阳,张玉林,周长银.基于复杂网络的基金加权网络结构分析[J].佳木斯大学学报(自然科学版).第29卷第1期.2011(1)：36-40.
[80]Kernighan B W, Lin S. A Efficient Heuristic Procedure for Partitioning Graphs [J]. Bell System Technical Journal.1970,49:291-307.
[81]Fiedler M. Algebraic connectivity of graphs. Czech. March. [J].1973,23:298
[82]Pethen A, Simon H, Liou K P. Partitioning Sparse Matrices with Eigenvectors of Graphs. SIAM J.Matrix Anal. Appl,1990,11:430.
[83]汪晓帆,刘亚冰.复杂网络中的社团结构算法综述.电子科技大学学报.2009,第38卷,第5期,537-543.
[84]Girvan M, Newman M E J. Community Structure in Social and Biological Networks[J]. Proc. Narl. Acad. Sci.2001.
[85]Wildinson D, Huberman B A. A Method for Finding Communities of Related Genes[J]. Proc Natl Acad SciUSA,2004,11:5241-5248.
[86]Tyler J, Wilkinson D, Huberman B. Email as Spectroscopy:Automated Discovery of Community Structure within Organizations. International Conference on Communities and Technologies,2003,81-96.
[87]Radicchi F, Castellano C, Cecconi F, Loreto V., Parisi D. Dedining and Identifying Communities in Networks [J]. Proc. Natl. Acad. Sci.,2004,101:2658-2663.
[88]Tsuchiura H, Ogata M, Tanaka Y, Kashiwaya S. Electronic States Around a Vortex Core in High-Tcsuperconductors Based on the T-J model [J]. Phy. Rev. B,2003,68:012509.
[89]Zhou H. Distance, Dissimilarity Index and Network Community Structure [J]. Phys. Rev. E,2003,67:061901.
[90]Fortunato S, Latora V, Marchiori M. A Method to Find Community Structures Based on Information Centrality [J]. Phys. Rev. E,2004,70:056104.
[91]Duch J, Arenas A. Communinty Detection in Complex Networks Using Extreme Optimization. Physical Review E,2005,72:027104.
[92]Danon L, Diaz Guilera A, Duch J, Arenas A. Comparing Community Strctrure Identification [J]. Stat. Mech,2005,09:P09008.
[93]Newman M E J. Fast Algorithm for Detecting Community Structure in Networks. Phys. Rev. E.2004,69:066133.
[94]Clauset A, Newman M E J, Moore C. Finding Community Structure in Very Large Networks [J]. Phys. Rev. E,2004,70:066111.
[95]Donetti L, Munoz M A. Detecting Network Communities:A New Systematic and Efficient Algorithm. Stat. Mech. Theor. Exp.,2004, P10012.
[96]Lancichinetti A, Fortunato S, Kertesz J. Detecting the Overlapping and Hierarchical Community Structure of Complex Networks[J]. New J. Phys.2009,11:033015.
[97]SHEN Hua-wei, CHENG Xue-qi, CAI Kai, et al. Detect Overlapping and Hierarchical Community Structure in Networks [J]. Physica A,2009,388(8):1706-1712.
[98]AHN Y-Y, Bagrow J P, Lehmann S. Communities and Hierarchical Organization of Links in Complex Networks[J/OL]. Eprint arXiv,2009,0903:3178. [2009-03-12]. http://www.arXiv.org.
[99]Palla G, Derrnyi I, Farkas I, et al, Uncovering the Overlapping Community Structure of Complex Networks in Nature and Society [J]. Nature,2005,435:814-818.
[100]Newman M E J, Girvan M. Finding and Evaluating Community Structure in Networks [J]. Phys. Rev. E,2004,69:026113.
[101]Newman M E J, Finding Community Structure in Networks Using the Eigenvectors of Matrices [J]. Physical Review E,2006,74:036104.
[102]Ccndon A, Karp R M. Algorithms for Graph Partitioning on the Planted Partition Model[J]. Random Struct. Algor,2001,18(2):116-140.
[103]Fan Y, LI M, Zhang P, et al. Accuracy and Precision of Methods for Community Identification in Weighted Networks[J]. Physica A,2007,377:363-372.
[104]Lancichinetti A, Fortunato S, Radicchi F. New Benchmark in Community Detection[J/OL]. Eprint arXiv,2008,0805:4770v2. [2009-04-16]. http://www. arXiv.org.
[105]Sawardecker E N, Sales-Pardos M, Amaral L A N. Detection of Node Group Membership in Networks with Group Overlap[J]. Eur Phys J B,2009,67:277.
[106]Dorngovtsev S N, Mendes J F F, Samukhin A N. Structure of Growing Networks with Preferential Linking[J]. Physical Review Letters,2000,85(21):4633-4636.
[107]Dorogovtsev S N, Mendes J F F. Samukhin A N. Size-dependent Degree Distribution of a Scale-free Network[J]. Physical Review E,2001,63(6):062101.
[108]Krapivsky P L, Redner S, Leyvraz F. Connectivity of Growing Random Networks[J]. Physical Review Letters,2000,85:4629-4632.
[109]Amaral L A N, Scala A, Barth618my Met al. Classes of Small-world Networks, Proc. Natl. Acad. Sci. USA,2000,97(21):11149-11152.
[110]Dorogovtscv S N, Mendes J F F. Evolution of Networks with Aging of Sites[J]. Physical Review E,2000,62:1842-1845.
[111]Albert, R., Barabasi, A.L. Topology of Evolving Networks:Local Events and Universaity[J]. Physical Review Letters,2000,85(24):5234-5237.
[112]Dorogovtsev S N, Mendes J. F. F. Scaling Behavior of Developing and Decaying Networks[J]. Europhys. Lett.2000,52:33-39.
[113]Bianconi G, Barabfisi A-L Competition and Multiscaling in Evolving Networks[J]. Europhys. Lett.2001,54:436442.
[114]Erghn G, Rodgers G J. Growing Random Networks with Fitness[J]. Physica A,2002, 303:261.272.
[115]Bianconi G, Barabasi A L. Bose-Einstein Condensation in Complex Networks[J].Phys. Rev. Lett,2001,86:5632-5635.
[116]Li X, Jin Y Y, Chen G. Complexity and Synchronization of the World Trade Web[J]. Physica A,2003,328:287-296.
[117]Li X, Chen G. A Local World Evolving Network Model[J]. Physica A 2003,328: 274-286.
[118]Zhang P, Li M, Mendes J F F, et al. Empirical Analysis and Evolving Model of Bipartite Networks[DR/eL]. [2009-11-13]. http://arxiv. org/abs/0804. 3854vl.
[119]Ferrer R, So16 R V, The Small-world of Human Language[J]. Proceedings of the Royal Society of London B,2001,268:2261-2265.
[120]M. E. J. Newman, S. H. Strogatz, and D. J. Watts. Random Graph Models of Social Networks. Phys. Rev. E 64,026118,2001.
[121]Ohkubo J, Tanaka K, Horiguchi T. Generation of Complex Bipartite Graphs by Using a Preferential Rewiring Process[J]. Physical Review E.2005,72:036120.
[122]O. Pulkkinen and J. Merikoski. Phase Transitions on Markovian Bipartite Graphs-an Application of the Zero-range Process. [J]. Stat. Phys.119,8812005.
[123]张培培,何阅,周涛等.一个描述合作网络顶点度分布的模型.物理学报,55,2006,60-67.
[124]M. Li, D. Wang, Y. Fan, Z. Di, J. Wu. Modelling Weighted Networks Using Connection Count[J]. New J. Phys.8 (2006) 72.
[125]M. Li, J. Wu, D. Wang, T. Zhou, Z. Di, Y. Fan. Evolving Model of Weighted Networks Inspired by Scientific Collaboration Networks[J]. Physica A 375 (2007) 355-364.
[126]潘四军,顾长贵,姜玉梅等.一个客运复合交通网动力学模型?.复杂系统与复杂性科学,5(4),84-88,2008.
[127]B.-B. Su, H. Chang, Y.-Z. Chen, D.-R. He. A Game Theory Model of Urban Public Traffic Networks[J]. Physica A 379,291-297 (2007).
[128]T. Zhou, B.-H. Wang, Y.-D. Jin, et al. Modeling Collaboration Networks Based on Nonlinear Preferential Attachment[J]. Int. J. Mod. Phys. C 18,297-314 (2007).
[129]章忠志,荣莉莉,周涛.一类无标度合作网络的演化模型.系统工程理论与实践.11,57-62,2005.
[130]Evans T S, Plato A D K. Exact Solution for the Time Evolution of Network Rewiring Models[J]. Physical Review E,2007,75:056-101.
[131]H Fan, Wang Z, Ohnishi T, et al. Multicommunity Weight-driven Bipartite Network Model[J]. Physical Review E,2008,78:026103.
[132]Ergun G. Human Sexual Contact Network as a Bipartite Graph[J]. Physica A,2002, 308:483-488.
[133]Guillaume J L, Latapy M. Bipartite Structure of All Complex Networks[J]. Information Processing Letters,2004,90:215-221.
[134]Ramasco J J, DorogovtBev S N, Pastor-Satorras R. Self-organization of Collaboration Networks[J]. Physical Review E,2004,70:036106.
[135]A. Ramezanpour, Europhys. Lett. Biology Helps to Construct Weighted Scale Free Networks.68,316,2004.
[136]Wang D H, Li z, Di z R. Bipartite Producer-Consumer Networks and the Size Distribution of Firms[J]. Physica A,2006,363:359-366.
[137]Lambiotte R, Ausloos M. Uncovering Collective Listening Habits and Music Genres in Bipartite Networks[J]. Physical Review E,2005,72:066107.
[138]Steven A Morris, Gary G Yen. Construction of Bipartite and Unipartite Weighted Networks form Collection of Journal Papers [OL].2006-12-28. http://arxiv.org/PS cache/physics/pdf/0503/0503061v1.pdf
[139]吴亚晶,张鹏,狄增如等.二分网络研究[J].复杂系统与复杂性科学.2010,第7卷第1期：1-12.
[140]Latapy M, Magnien C, Vecchio N D. Basic Notions for the Analysis of Large Two Mode Networks[J]. Social Networks,2008,30:3148.
[141]Li X, Chen, G-R. A Local-World Evolving Network Model [J]. Physica A.2003, 328(1-2):274-286.
[142]Albert R, Barabasi A L. Statistical Mechanics of Complex Networks [J]. Rev. Mod. Phys.,2002,74:47-97.
[143]WATTS D J, STROGATZ S H. Collective Dynamics of Small-Word Networks[J]. Nature,1998,393:440-442.
[144]Newman M E J. The Structure and Function of Complex Networks [J]. SIAM Review, 2003,45(2):167-256.
[145]Latora V, Marchiori M. Economic Small-World Behavior in Weighted Networks [J]. Eur Phys J B,2003,32; 249.
[146]Diego Garlaschelli, Stefano Battiston, Maurizio Castric, et al. Servedio, Guido Aldarelli:the Scale-Free Topology of Market Investments[J]. Physica A,2005,350: 491.
[147]Albert, R., Barabasi, A.L. Topology of Evolving Networks:Local Events and Universality. Physical Review Letters,2000,85(24):5234-5237.