产业复杂网络的建模、仿真与分析
|
摘要
本文的产业复杂网络既包括产业竞争关系复杂网络,还包括新出现的大众生产的合作关系复杂网络。企业本来就是存在于由大量竞争对手形成的大规模网络之中的。产业竞争关系复杂网络模型及分析方法的提出,为经典的产业组织分析补充了企业之间竞争关系的网络视角,从而发展了产业组织的理论与方法。但是已有的产业复杂网络研究大都仅针对竞争关系复杂网络的,本文的研究对象则既包括产业竞争关系复杂网络,还包括了大众生产合作关系复杂网络。
而且目前的产业竞争关系的复杂网络分析,大多是针对具体的单个产业进行的,缺少针对所有产业的普适的分析框架与方法,本文首先通过对多个具体的产业竞争关系复杂网络以及大众生产合作关系网络的分析,归纳出具有普适性的产业复杂网络分析的“静态拓扑特征—子图特征—动态生成机制—动力学性质”的分析框架。其次,深入探讨并提出了各种产业复杂网络的建模、仿真与分析的具体方法。
在静态拓扑分析中,采用极大似然方法分析了产业复杂网络的度分布;在子图特征分析中,采用了k-clique子图、模体、层级结构、集团结构、分形与多重分形等分析方法;在动态生成机制分析中,通过建构模体异向匹配模型、拟Yule增长模型、双向适应度模型来揭示各种产业复杂网络的生成机理;在网络动力学性质分析中,构建了产业竞争关系复杂网络上的竞争扩散模型、大众生产平台之间的竞争模型、大众生产合作关系网络上的信息传播模型与多智能体模型、以及Ising模型与多智能体自适应模型等模型来进行研究。这些模型上不仅有方法方面来自于“综合”的创新性,也更加符合实际,比如多智能体模型将复杂网络中的“死”的节点视为“活”的智能体,将复杂自适应系统分析方法引进产业复杂网络的分析之中,使得产业复杂网络的分析方法考虑了企业实际上所具有的自主性。再次,在模型分析过程中还对相关的算法做了改进。比如在产业复杂网络的静态结构研究中,采用Powell着色法改进了复杂网络分形的盒维数算法;在产业复杂网络上的动力学性质研究中改进了粒子群算法等等。
最后,需要指出的是以上框架、模型与方法不仅具有产业复杂网络分析方法方面的普适意义,而且具有新的洞察力,因此对产业复杂网络以及产业分析有一些新的发现。比如用极大似然方法估计出的产业复杂网络度分布的r_(mian)值,揭示了产业复杂网络满足幂律分布的企业最小竞争对手的数目,度的幂律分布刻画了产业内企业竞争对手数目的异质性以及大众生产者合作者数目的异质性。产业复杂网络的子图、模体、集团、分形与多重分形分析的发现,分别揭示了产业竞争存在着稳定与重叠的竞争结构,具有层级性,集团特征以及自相似等等特性。生成机制与网络上的动力机制分析也得出网络生成与竞争扩散等等方面的有关发现。
The industry complex network in the paper include the industry competition complex net-work and the emerging collaboration network based on Peer Production. In fact, enterprisesexist in large networks formed by many competitors. Industry competition complex networkmodel and the analytical method complement the classical Organization Analysis theory fromnetwork perspective among the enterprises, which develops the industrial organization theoryand method. However,most industry complex network analysis focuses on competition net-work, the paper will both study the industry competition complex network and Peer Productionnetwork.
In addition, the research on industry complex network mostly focus on single industryand lack general analytical framework and methods to all industries. First of all, through theanalysis of many specific real competition network and Peer Production network, the paperconstruct a universal framework of industry competition complex network for”static topologycharacteristics—subgraph characteristics—generating mechanism—dynamic characteristics”.
Second, we make deep study on the static characteristics of the network topology, mainlyincluding the application of maximum likelihood method to estimate the degree distribution ofindustry complex networks, investigating the static structure especially the subgraph charac-teristic of industry complex network by the analysis of k-clique subgraph, motif, hierarchicalstructure, community structure, fractal and multifractal property. We propose the motif dis-assortative model, the imitated Yule process model and the bipartite fitness model to analyzethe generating mechanism of complex network. Again, we make research on the dynamicproperty of the industry competition network and Peer Production collaboration network. Weconstruct the competition spread model over the industry competition network and find thatThe enterprise location in the network topology who launch the competition have a significanteffect on the spread result. We also find that competitive effects spreading over the network haslocal characteristic. we construct and analyze the platform competition model of peer produc-tion,which reveals the evolution of peer production platform competition when the competitionintensity based on the network topology follows the power law and Gaussian distribution. Wefurther construct the information spread model based on Peer Production collaboration networkand analyze topological property of the individual who initiate the information as well as thenumber impact significantly on the spread result. Then we construct the multi-agent adaptivesystem model to study the information spread process and reveal the macro emergence of theadaptive system during different process. We also analyze the stability of Peer Production by constructing Ising model combining herding effect and study the the critical point of the sys-tem impacted by different network structures and external conditions, and finally we use MonteCarlo simulation to verify the critical analytical solution derived by mean field theory. We con-struct multi-agent self-adaptive system and analyze the stability of peer production system inshort term and long term. On the research of network dynamics, we construct the competitionspread model, Peer Production platform competition model, information spread based on PeerProduction network and multi-agent model, Ising model and multi-agent model, which are notonly”comprehensive”innovative but also more realistic, for example multi-agent model con-sider the”dead”node as a”live”agent, it bring the complex adaptive system into the analysisof industry complex network which make the industry complex network method concern theenterprises’practical autonomy. Further, During the analysis process of the static and dynamiccharacteristics of the network, we improve the corresponding algorithm. For example in theanalysis of static network topology, we improve the traditional box covering algorithm for com-plex network fractal property analysis and verify the efficiency of the the improved algorithmand in the process of dynamics analysis modeling, we improve PSO from the perspective ofstatic network topology and dynamic network topology, propose PSO based on SFL and DSF-PSO two improved models.
Finally, be noted that the above framework, model and approach not only has the indus-try’s complex network analysis universal significance, but also has the new insights into theindustry complex network and industry analysis. For example we adopt the maximum likeli-hood method to estimate the r_(min) values of the industry complex network’s degree distributionwhich reveal the smallest competitors numbers of power-law distribution, and the degree fol-low the power-law distribution depict the heterogeneity within competitors of industry complexnetwork and heterogeneity within Collaborators of Peer Production network. The discoveryof subgraph, motif, community structure, fractal and multifractal property in industry complexnetwork respectively reveals the existence of a stable industrial competition and overlappingcompetition structure, with hierarchical, community characteristics, and self-similarity and soon.
而且目前的产业竞争关系的复杂网络分析,大多是针对具体的单个产业进行的,缺少针对所有产业的普适的分析框架与方法,本文首先通过对多个具体的产业竞争关系复杂网络以及大众生产合作关系网络的分析,归纳出具有普适性的产业复杂网络分析的“静态拓扑特征—子图特征—动态生成机制—动力学性质”的分析框架。其次,深入探讨并提出了各种产业复杂网络的建模、仿真与分析的具体方法。
在静态拓扑分析中,采用极大似然方法分析了产业复杂网络的度分布;在子图特征分析中,采用了k-clique子图、模体、层级结构、集团结构、分形与多重分形等分析方法;在动态生成机制分析中,通过建构模体异向匹配模型、拟Yule增长模型、双向适应度模型来揭示各种产业复杂网络的生成机理;在网络动力学性质分析中,构建了产业竞争关系复杂网络上的竞争扩散模型、大众生产平台之间的竞争模型、大众生产合作关系网络上的信息传播模型与多智能体模型、以及Ising模型与多智能体自适应模型等模型来进行研究。这些模型上不仅有方法方面来自于“综合”的创新性,也更加符合实际,比如多智能体模型将复杂网络中的“死”的节点视为“活”的智能体,将复杂自适应系统分析方法引进产业复杂网络的分析之中,使得产业复杂网络的分析方法考虑了企业实际上所具有的自主性。再次,在模型分析过程中还对相关的算法做了改进。比如在产业复杂网络的静态结构研究中,采用Powell着色法改进了复杂网络分形的盒维数算法;在产业复杂网络上的动力学性质研究中改进了粒子群算法等等。
最后,需要指出的是以上框架、模型与方法不仅具有产业复杂网络分析方法方面的普适意义,而且具有新的洞察力,因此对产业复杂网络以及产业分析有一些新的发现。比如用极大似然方法估计出的产业复杂网络度分布的r_(mian)值,揭示了产业复杂网络满足幂律分布的企业最小竞争对手的数目,度的幂律分布刻画了产业内企业竞争对手数目的异质性以及大众生产者合作者数目的异质性。产业复杂网络的子图、模体、集团、分形与多重分形分析的发现,分别揭示了产业竞争存在着稳定与重叠的竞争结构,具有层级性,集团特征以及自相似等等特性。生成机制与网络上的动力机制分析也得出网络生成与竞争扩散等等方面的有关发现。
The industry complex network in the paper include the industry competition complex net-work and the emerging collaboration network based on Peer Production. In fact, enterprisesexist in large networks formed by many competitors. Industry competition complex networkmodel and the analytical method complement the classical Organization Analysis theory fromnetwork perspective among the enterprises, which develops the industrial organization theoryand method. However,most industry complex network analysis focuses on competition net-work, the paper will both study the industry competition complex network and Peer Productionnetwork.
In addition, the research on industry complex network mostly focus on single industryand lack general analytical framework and methods to all industries. First of all, through theanalysis of many specific real competition network and Peer Production network, the paperconstruct a universal framework of industry competition complex network for”static topologycharacteristics—subgraph characteristics—generating mechanism—dynamic characteristics”.
Second, we make deep study on the static characteristics of the network topology, mainlyincluding the application of maximum likelihood method to estimate the degree distribution ofindustry complex networks, investigating the static structure especially the subgraph charac-teristic of industry complex network by the analysis of k-clique subgraph, motif, hierarchicalstructure, community structure, fractal and multifractal property. We propose the motif dis-assortative model, the imitated Yule process model and the bipartite fitness model to analyzethe generating mechanism of complex network. Again, we make research on the dynamicproperty of the industry competition network and Peer Production collaboration network. Weconstruct the competition spread model over the industry competition network and find thatThe enterprise location in the network topology who launch the competition have a significanteffect on the spread result. We also find that competitive effects spreading over the network haslocal characteristic. we construct and analyze the platform competition model of peer produc-tion,which reveals the evolution of peer production platform competition when the competitionintensity based on the network topology follows the power law and Gaussian distribution. Wefurther construct the information spread model based on Peer Production collaboration networkand analyze topological property of the individual who initiate the information as well as thenumber impact significantly on the spread result. Then we construct the multi-agent adaptivesystem model to study the information spread process and reveal the macro emergence of theadaptive system during different process. We also analyze the stability of Peer Production by constructing Ising model combining herding effect and study the the critical point of the sys-tem impacted by different network structures and external conditions, and finally we use MonteCarlo simulation to verify the critical analytical solution derived by mean field theory. We con-struct multi-agent self-adaptive system and analyze the stability of peer production system inshort term and long term. On the research of network dynamics, we construct the competitionspread model, Peer Production platform competition model, information spread based on PeerProduction network and multi-agent model, Ising model and multi-agent model, which are notonly”comprehensive”innovative but also more realistic, for example multi-agent model con-sider the”dead”node as a”live”agent, it bring the complex adaptive system into the analysisof industry complex network which make the industry complex network method concern theenterprises’practical autonomy. Further, During the analysis process of the static and dynamiccharacteristics of the network, we improve the corresponding algorithm. For example in theanalysis of static network topology, we improve the traditional box covering algorithm for com-plex network fractal property analysis and verify the efficiency of the the improved algorithmand in the process of dynamics analysis modeling, we improve PSO from the perspective ofstatic network topology and dynamic network topology, propose PSO based on SFL and DSF-PSO two improved models.
Finally, be noted that the above framework, model and approach not only has the indus-try’s complex network analysis universal significance, but also has the new insights into theindustry complex network and industry analysis. For example we adopt the maximum likeli-hood method to estimate the r_(min) values of the industry complex network’s degree distributionwhich reveal the smallest competitors numbers of power-law distribution, and the degree fol-low the power-law distribution depict the heterogeneity within competitors of industry complexnetwork and heterogeneity within Collaborators of Peer Production network. The discoveryof subgraph, motif, community structure, fractal and multifractal property in industry complexnetwork respectively reveals the existence of a stable industrial competition and overlappingcompetition structure, with hierarchical, community characteristics, and self-similarity and soon.
引文
[1] WATTS D J, STROGATZ S H. Collective dynamics of’small-world’networks[J]. Nature,1998, 393:440–442.
[2] BARAB A′SI A L, ALBERT R. Emergence of scaling in random networks[J]. Science,1999, 286:509–512.
[3]陈关荣.复杂网络及其新近研究进展简介[J].力学进展, 2008, 38(6):653–662.
[4] YANG J, LU L, XIE W, et al. On competitive relationship networks: A new method forindustrial competition analysis[J]. Physica A: Statistical Mechanics and its Applications,2007, 382(2):704– 714.
[5]杨建梅,陆履平,谢王丹.广州软件企业竞争关系的复杂网络分析[C]//第二届全国复杂动态网络学术论坛论文集.北京,中国:中国高等科学技术中心,2005:616–619.
[6] YANG J, WANG W, CHEN G. A two-level complex network model and its applica-tion[J]. Physica A: Statistical Mechanics and its Applications, 2009, 388(12):2435–2449.
[7] ZHUANG D, YANG J. Simulation of Rivalry Spread Effect over the Competitive Pres-sure Network[C]//Proceeding of the 2008 IEEE International Conference on Systems,Man, and Cybernetics. Suntec Singapore: IEEE, 2008:851–855.
[8]庄东.基于复杂网络的产业内厂商间竞争关系的建模与仿真[D].广州:华南理工大学, 2007.
[9]贝塔朗菲.一般系统论:基础、发展和应用[M].北京:清华大学出版社, 1987.
[10]戴汝为.复杂巨系统科学―一门21世纪的科学[J].自然杂志, 1997, 19 (4):187–192.
[11]霍兰J H.隐秩序-适应性造就复杂性[M].上海:上海科技教育出版社, 2001.
[12]于景元,涂元季.从定性到定量综合集成方法―案例研究[J].系统工程的理论与实践, 2002, 5:1–7.
[13]于景元,周晓纪.从定性到定量综合集成方法的实现和应用[J].系统工程理论与实践, 2002, 10:28–30.
[14]于景元.从综合集成方法思想到综合集成实践[J].管理学报, 2005, 1:4–10.
[15]汪小帆,李翔,陈关荣.复杂网络:理论及其应用[M].北京:清华大学出版社, 2006.
[16] WATTS D J, STROGATZ S H. Collective dynamics of’small-world’networks[J]. Nature,1998, 393:440–442.
[17] NEWMAN M E J, WATTS D J. Renormalization group analysis of the small-worldnetwork model[J]. Physics Letters A, 1999, 263(4-6):341– 346.
[18] DOROGOVTSEV S N, MENDES J F. Evolution of Networks[J]. Advances in Physics,2002, 51(4):1079–1187.
[19] KLEINBERG J M. Navigation in a small world[J]. Nature, 2001, 406:845.
[20] ALBERT R, BARAB A′SI A L. Topology of Evolving Networks: Local Events and Uni-versality[J]. Physical Review Letters, 2000, 85(24):5234–5237.
[21]郭雷,许晓鸣.复杂网络[M].上海:科技教育出版社, 2006.
[22] LUCE R. Connectivity and generalized n-cliques in sociometric group structure[J]. Psy-chometrika, 1950, 15:169–190.
[23] BRON C, KERBOSCH J. Finding all n-cliques of an undirected graph[J]. Comm of theACM, 16:575–577.
[24] TOMITA E, TANAKA A, TAKAHASHI H. The worst-case time complexity for generatingall maximal cliques and computational experiments[J]. Theoretical Computer Science,2006, 363 (1):28–42.
[25] TOMITA E, KAMEDA T. An efficient branch-and-bound algorithm for finding a maxi-mum clique with computational experiments[J]. Journal of Global Optimization, 2007,37 (1):95–111.
[26] BARAB A′SI A L, OLTVAI Z N. Network biology: understanding the cell’s functionalorganization[J]. Nature Reviews-Genetics, 2004, 5:101–114.
[27] MILO R, SHEN O S, ITZKOVITZ S, et al. Network motifs: Simpler building blocks ofcomplex networks[J]. Science, 2002, 298:824.
[28] SHEN O S, MILO R, MANGAN S, et al. Network motifs in the transcriptional regulationnetwork of Escherichia coli[J]. Nature Genetics, 2002, 31:64.
[29] SONG C, HAVLIN S, MAKSE H A. Origins of fractality in the growth of complexnetworks[J]. NATURE PHYSICS, 2006, 2:275.
[30] SONG C, HAVLIN S, MAKSE H A. Self-similarity of complex networks[J]. Nature,2005, 433:392.
[31] SONG C, GALLOS L K, HAVLIN S, et al. How to calculate the fractal dimension ofa complex network: the box covering algorithm[J]. Journal of Statistical Mechanics:Theory and Experiment, 2007, 2007(03):P03006.
[32] TAKEMOTO K, OOSAWA C, AKUTSU T. Structure of n-clique networks embeddedin a complex network[J]. Physica A: Statistical Mechanics and its Applications, 2007,380:665– 672.
[33] PALLA G, DERENYI I, FARKAS I, et al. Uncovering the overlapping community struc-ture of complex networks in nature and society[J]. Nature, 2005, 435:814–818.
[34] V A′ZQUEZ A, DOBRIN R, SERGI D, et al. The Topological Relationship between theLarge-Scale Attributes and Local Interaction Patterns of Complex Networks[J]. Pro-ceedings of the National Academy of Sciences of the United States of America, 2004,101(52):17940–17945.
[35] RAVASZ E, BARAB A′SI A L. Hierarchical organization in complex networks[J]. Phys.Rev. E, 2003, 67(2):026112.
[36] TAKEMOTO K, OOSAWA C. Evolving networks by merging cliques[J]. Phys. Rev. E,2005, 72(4):046116.
[37] PALLA G, BARABASI A L, VICSEK T. Quantifying social group evolution[J]. Nature,2007, 446:664–667.
[38] GOLTSEV A V, DOROGOVTSEV S N, MENDES J F F. ?? -core (bootstrap) percolationon complex networks: Critical phenomena and nonlocal effects[J]. Phys. Rev. E, 2006,73(5):056101.
[39] PETTIE S, RAMACHANDRAN V. An optimal minimum spanning tree algorithm[J]. J.ACM, 2002, 49(1):16–34.
[40] PETTIE S, RAMACHANDRAN V. A Randomized Time-Work Optimal Parallel Algo-rithm for Finding a Minimum Spanning Forest[J]. SIAM J. Comput., 2002, 31(6):1879–1895.
[41] BADER D A, CONG G. Fast shared-memory algorithms for computing the minimumspanning forest of sparse graphs[J]. J. Parallel Distrib. Comput., 2006, 66(11):1366–1378.
[42] GIBSON D, KLEINBERG J, RAGHAVAN P. Inferring Web communities from link topol-ogy[C]//Proceeding of the 9th ACM Conference on Hypertext and Hypermedia. NewYork, USA: ACM, 1998:225–234.
[43] FLAKE G W, LAWRENCE S R, GILES C L, et al. Self-organization and identificationof Web communities[J]. IEEE Computer, 2002, 35:66–71.
[44] ADAMIC L A, ADAR E. Friends and neighbors on the Web[J]. Social Networks, 2003,25(3):211–230.
[45] HOLME P, HUSS M, JEONG H. Subnetwork hierarchies of biochemical pathways[J].Bioinformatics, 2003, 19:532.
[46] WILKINSON D M, HUBERMAN B A. A method for finding communities of relatedgenes[J]. Proceedings of the National Academy of Sciences of the United States ofAmerica, 2004, 101(Suppl 1):5241–5248.
[47] GIRVAN M, NEWMAN M E J. Community structure in social and biological net-works[J]. Proc. Natl. Acad. Sci. USA, 2002, 99:7821–7826.
[48] GLEISER P, DANON L. Community structure in Jazz[J]. Advances in Complex Systems,2003, 6:565–573.
[49] NEWMAN M E J. Modularity and community structure in networks[J]. Proc. Natl.Acad. Sci. USA, 2006, 103:8577.
[50] NEWMAN M E J. Finding community structure in networks using the eigenvectors ofmatrices[J]. Physical Review E, 2006, 74:036104.
[51] NEWMAN M E J. Detecting community structure in networks[J]. The European PhysicalJournal B-Condensed Matter, 2004, 38:321–330.
[52] NEWMAN M E J. Fast algorithm for detecting community structure in networks[J].Physical Review E, 2004, 69:066133.
[53] LI X, CHEN G. A local-world evolving network model[J]. Physica A: Statistical Me-chanics and its Applications, 2003, 328(1-2):274– 286.
[54] LIU Z, LAI Y C, YE N, et al. Connectivity distribution and attack tolerance of generalnetworks with both preferential and random attachments[J]. Physics Letters A, 2002,303(5-6):337–344.
[55] RAMASCO J J, DOROGOVTSEV S N, PASTOR-SATORRAS R. Self-organization of col-laboration networks[J]. Phys. Rev. E, 2004, 70(3):036106.
[56] FAN Z, CHEN G, ZHANG Y. A comprehensive multi-local-world model for complexnetworks[J]. Physics Letters A, 2009, 373(18-19):1601–1605.
[57]方锦清,李永.网络科学中统一混合理论模型的若干研究进展[J].力学进展, 2008,38:663–678.
[58] ZHU C P, ZHOU T, YANG H J, et al. The process of coevolutionary competitive ex-clusion: speciation, multifractality and power-laws in correlations[J]. New Journal ofPhysics, 2008, 10(2):023006 (10pp).
[59] WU Z X, XU X J, WANG Y H. Maximal planar networks with large clustering coeffi-cient and power-law degree distribution[J]. Phys. Rev. E, 2006, 73(5):058101.
[60] WANG W X, WANG B H, HU B, et al. General Dynamics of Topology and Traffic onWeighted Technological Networks[J]. Phys. Rev. Lett., 2005, 94(18):188702.
[61] WANG W X, HU B, ZHOU T, et al. Mutual selection model for weighted networks[J].Phys. Rev. E, 2005, 72(4):046140.
[62] OU Q, JIN Y D, ZHOU T, et al. Power-law strength-degree correlation from resource-allocation dynamics on weighted networks[J]. Phys. Rev. E, 2007, 75(2):021102.
[63] ZHOU T, REN J, MEDO M C V, et al. Bipartite network projection and personal recom-mendation[J]. Phys. Rev. E, 2007, 76(4):046115.
[64] BARRAT A, BARTHE′LEMY M, VESPIGNANI A. Weighted Evolving Networks: Cou-pling Topology and Weight Dynamics[J]. Phys. Rev. Lett., 2004, 92(22):228701.
[65] FAN Y, LI M, CHEN J, et al. Network of Econophysicists: a weighted network to in-vestigate the development of Econophysics[J]. International Journal of Modern PhysicsB, 2004, 18:17–19.
[66] ZHANG P, LI M, WU J, et al. The analysis and dissimilarity comparison of communitystructure[J]. Physica A: Statistical Mechanics and its Applications, 2006, 367:577–585.
[67] FAN Y, LI M, ZHANG P, et al. Accuracy and precision of methods for communityidentification in weighted networks[J]. Physica A: Statistical Mechanics and its Appli-cations, 2007, 377(1):363– 372.
[68] LI M, FAN Y, WANG D, et al. Small-world effect induced by weight randomization onregular networks[J]. Physics Letters A, 2007, 364(6):488– 493.
[69] FAN Y, LI M, ZHANG P, et al. The effect of weight on community structure of net-works[J]. Physica A: Statistical Mechanics and its Applications, 2007, 378(2):583–590.
[70] LI M, WANG D, FAN Y, et al. Modelling weighted networks using connection count[J].New Journal of Physics, 2006, 8(5):72.
[71] LI M, WU J, WANG D, et al. Evolving model of weighted networks inspired by scien-tific collaboration networks[J]. Physica A: Statistical Mechanics and its Applications,2007, 375(1):355– 364.
[72] LIU Z, HU B. Epidemic spreading in community networks[J]. EPL (Europhysics Let-ters), 2005, 72(2):315–321.
[73] WU X, LIU Z. How community structure in?uences epidemic spread in social net-works[J]. Physica A: Statistical Mechanics and its Applications, 2008, 387(2-3):623–630.
[74] HUANG W, LI C. Epidemic spreading in scale-free networks with communitystructure[J]. Journal of Statistical Mechanics: Theory and Experiment, 2007,2007(01):P01014.
[75] ZHENG D F, HUI P, TRIMPER S, et al. Epidemics and dimensionality in hierarchicalnetworks[J]. Physica A: Statistical Mechanics and its Applications, 2005, 352(2-4):659– 668.
[76] ZHOU T, LIU J G, BAI W J, et al. Behaviors of susceptible-infected epidemics onscale-free networks with identical infectivity[J]. Phys. Rev. E, 2006, 74(5):056109.
[77] YANG R, WANG B H, REN J, et al. Epidemic spreading on heterogeneous networkswith identical infectivity[J]. Physics Letters A, 2007, 364(3-4):189– 193.
[78] YANG R, ZHOU T, XIE Y B, et al. Optimal contact process on complex networks[J].Phys. Rev. E, 2008, 78(6):066109.
[79] XU X J, WANG W X, ZHOU T, et al. Geographical effects on epidemic spreading inscale-free networks[J]. International Journal of Modern Physics C, 2006, 17:1815.
[80] XU X J, ZHANG X, MENDES J F F. Impacts of preference and geography on epidemicspreading[J]. Physical Review E, 2007, 76:056109.
[81] ZHOU J, LIU Z. Epidemic spreading in communities with mobile agents[J]. Physica A:Statistical Mechanics and its Applications, 2009, 388(7):1228– 1236.
[82] BAI W J, ZHOU T, WANG B H. Immunization of Susceptible-Infected Model on Scale-Free networks[J]. Physica A, 2007, 384:656–662.
[83] HAN X P. Disease spreading with epidemic alert on small-world networks[J]. PhysicsLetters A, 2007, 365(1-2):1–5.
[84] SMALL M, TSE C. Clustering model for transmission of the SARS virus: applicationto epidemic control and risk assessment[J]. Physica A: Statistical Mechanics and itsApplications, 2005, 351(2-4):499– 511.
[85] YAN G, ZHOU T, HU B, et al. Efficient routing on complex networks[J]. Phys. Rev. E,2006, 73(4):046108.
[86] MOTTER A E, ZHOU C, KURTHS J. Network synchronization, diffusion, and the para-dox of heterogeneity[J]. Phys. Rev. E, 2005, 71(1):016116.
[87] ZHOU C, MOTTER A E, KURTHS J. Universality in the Synchronization of WeightedRandom Networks[J]. Phys. Rev. Lett., 2006, 96(3):034101.
[88] ZHOU C, KURTHS J. Dynamical Weights and Enhanced Synchronization in AdaptiveComplex Networks[J]. Phys. Rev. Lett., 2006, 96(16):164102.
[89] WANG X, CHEN G. Synchronization in scale-free dynamical networks: robustness andfragility[J]. IEEE Trans. Circuits and Systems-I, 2002, 49:54–62.
[90] LI X, CHEN G R. Synchronization and desynchronization of complex dynamicalnetworks: an eigineering viewpoint[J]. IEEE Trans. Circuits and Systems-I, 2003,50:1381–1390.
[91] ZHAO M, ZHOU T, WANG B H, et al. Relations between average distance, heterogene-ity and network synchronizability[J]. Physica A: Statistical and Theoretical Physics,2006, 371(2):773– 780.
[92] XIANG W, BING-HONG W, TAO Z, et al. Synchronizability of Highly Clustered Scale-Free Networks[J]. Chinese Physics Letters, 2006, 23(4):1046–1049.
[93] ZHOU T, ZHAO M, CHEN G, et al. Phase synchronization on scale-free networks withcommunity structure[J]. Physics Letters A, 2007, 368(6):431– 434.
[94]吕金虎.复杂动力网络的数学模型与同步准则[J].系统工程理论与实践, 2004,4:17–22.
[95]吕金虎.复杂网络的同步:理论、方法、应用与展望[J].力学进展, 2008, 6:713–722.
[96] ZHAO M, ZHOU T, WANG B H, et al. Enhance synchronizability by structural pertur-bations[J]. Physical Review E, 2005, 72:057102.
[97] ZHAO M, ZHOU T, WANG B H, et al. Better synchronizability predicted by a newcoupling method[J]. The European Physical Journal B, 2006, 53:375.
[98] ZHOU T, ZHAO M, WANG B H. Better synchronizability predicted by crossed doublecycle[J]. Phys. Rev. E, 2006, 73(3):037101.
[99] WANG B, ZHOU T, XU Z L, et al. Optimizing synchronizability of networks[J]. Eur.Phys. J. B, 2007, 60:89–95.
[100] QIANG G, JIAN-GUO L, RUI-LI W, et al. Improvement of Synchronizability of Scale-Free Networks[J]. Chinese Physics Letters, 2007, 24(8):2437–2440.
[101] LI M, FAN Y, CHEN J, et al. Weighted networks of scientific communication: themeasurement and topological role of weight[J]. Physica A: Statistical Mechanics and itsApplications, 2005, 350(2-4):643– 656.
[102] ZHANG P P, CHEN K, HE Y, et al. Model and empirical study on some collaborationnetworks[J]. Physica A: Statistical Mechanics and its Applications, 2006, 360(2):599–616.
[103] CHANG H, SU B B, LIU C P, et al. Community, Hierarchy and Interweavement in Col-laboration Networks[J]. International Journal of Modern Physics C, 2008, 19(10):1537–1554.
[104]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.
[105] HU H, WANG X. Evolution of a large online social network[J]. Physics Letters A, 2009,373(12-13):1105– 1110.
[106] HU H B, WANG X F. Disassortative mixing in online social networks[J]. EurophysicsLetters, 2009, 86(1):18003.
[107] 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.
[108]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.
[109] CHEN Y Z, FU C H, CHANG H, et al. Connectivity correlations in three topologicalspaces of urban bus-transport networks in China[J]. Chin. Phys. B, 2008, 18:3580–3587.
[110] RU W, XU C. Hierarchical Structure, Disassortativity and Information Measures of theUS Flight Network[J]. Chinese Physics Letters, 2005, 22(10):2715–2718.
[111] 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).
[112] LIU J, DANG Y, WANG Z, et al. Relationship between the in-degree and out-degree ofWWW[J]. Physica. A, 2006, 371:861–869.
[113]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):3916–3921.
[114]胡鲜.基于复杂网络的中国汽车零部件企业竞争关系结构及行为研究[D].广州:华南理工大学, 2008.
[115]后锐,杨建梅,姚灿中.物流产业竞争关系的复杂网络模型研究[J].管理学报,2010, 7(3):1–6.
[116]刘浩.广州软件企业固话网络的增长机制研究[D].广州:华南理工大学, 2008.
[117]汤玮亮.百度百科的复杂网络建模与分析-大众生产视角[D].广州:华南理工大学, 2007.
[118]吴在伟.在线百科稳定性研究[D].广州:华南理工大学, 2009.
[119]潘向东.开源社区自组织演化问题研究[D].广州:华南理工大学, 2009.
[120] JIANMEI Y, HUANG X, ZHUANG D, et al. The Complex Network Analysis ofCompetitive Relationships Between Manufacturers in Foshan Ceramic Industry Clus-ter[C]//Proceedings of The 2006 International Conference on Management Science andEngineering (13th). Lille, France: Harbin Institute of Technology Press, 2006,II:1020–1023.
[121] TANG S H, YANG J, YAO C. Study on the Effect of Knowledge Diffusion on VirtualSocial-relationship Networks-Taking Book Inquiry as Example[C]//. Beijing: IEEE.Press, 2008:764–767.
[122]杨建梅,乐建兵.基于产业集群的企业重点投资地区决策的仿真[J].管理工程学报, 2005, 19(2):146–149.
[123]乐建兵,杨建梅,赵海霞.社会学仿真评述[J].科技管理研究, 2005, 12:263–267.
[124]乐建兵.基于多智能体仿真的广东产业集群成长机制研究[D].广州:华南理工大学, 2005.
[125]王铁,胡卫国.论中国汽车零部件产业组织政策[J].汽车工业研究, 2006, 11:6–12.
[126]王永祥,寇平均,楼志刚.我国汽车零部件产业的发展策略探讨[J].汽车工业研究, 2006, 2:20–22.
[127]李纪珍,贾永轩.汽车零部件整合[M].北京:机械工业出版社, 2006.
[128] HIPPEL E V, KROGH G V. Open Source Software and the”Private-Collective”Innova-tion Model: Issues for Organization Science[J]. Organization Science, 2003, 14(2):209–223.
[129]郭宇飚.知识经济中一种新的产权制度和生产方式――基于开源代码软件现象的研究[D].北京:北京大学, 2004.
[130] LERNER J, TIROLE J. Some Simple Economics of Open Source[J]. J.Indust.Econom.,2002, 50(2):1–55.
[131] DAVID P, BRADFORD C B.”Peer production”Promises to Leap in Importance[J].Information Week., 2002, 7:741.
[132] BENKLER Y. The Battle Over The Institutional Ecosystem in the Digital Environ-ment[J]. Communications of the ACM, 2002, 44(2):84–90.
[133] CORNEL J, KROWNE A. A Scholia - Based Document Model For Commons - BasedPeer Production[R]. Atlanta, USA: Proceedings of the Symposium on Free Culture andthe Digital, 2005.
[134] BENKLER Y. Coase’s penguin[J]. The Yale Law Journal, 2002, 112(3):369–446.
[135] BENKLER Y. Commons-based peer production and virture[J]. The Journal of PoliticalPhilosophy, 2006, 14(4):394–419.
[136] COASE R. The Nature of the Firm[J]. Economica, 1937, 4(16):386–405.
[137] WILLIAMSON O E, WINTER S G. The Nature of the Firm: Origins, Evolution, andDevelopment[M]. USA: Oxford University, 1993.
[138] TAPSCOTT D, WILLIAMS D, A. Wikinomics: How Mass Collaboration Changes Ev-erything[M]. New York: Portfolio Hardcover, 2007.
[139]王林,戴冠中.复杂网络的Scale-Free性、Scale-Free现象及其控制[M].北京:科学出版社, 2009.
[140] CLAUSET A, SHALIZI C R, NEWMAN M E J. Power-law distributions in empiricaldata[J]. SIAM Review, 2009, 51:661.
[141] GOLDSTEIN M L, MORRIS S A, YEN G G. Problems with fitting to the power-lawdistribution[J]. The European Physical Journal B - Condensed Matter and ComplexSystems, 2004, 41:255–258.
[142] SHALIZI C R. Maximum Likelihood Estimation for q-Exponential (Tsallis) Distribu-tions[J]. 2007.
[143] BAUKE H. Parameter estimation for power-law distributions by maximum likelihoodmethods[J]. The European Physical Journal B - Condensed Matter and Complex Sys-tems, 2007, 58:167–173.
[144] LAHERRE′RE J, SORNETTE D. Stretched exponential distributions in nature and econ-omy:“fat tails”with characteristic scales[J]. The European Physical Journal B - Con-densed Matter and Complex Systems, 1998, 2 2:525–539.
[145]王文杰.中国家电产业竞争关系复杂网络分析[D].广州:华南理工大学, 2006.
[146]汤玮亮.百度百科的复杂网络建模与分析-大众生产视角[D].广州:华南理工大学, 2007.
[147] DERE′NYI I, PALLA G, VICSEK T. Clique Percolation in Random Networks[J]. Phys.Rev. Lett., 2005, 94(16):160202.
[148] PALLA G, DERE′NYI I, FARKAS I, et al. Uncovering the overlapping community struc-ture of complex networks in nature and society[J]. Nature, 2005, 435:814–818.
[149] HARTWELL L H, HOPFIELD J J, LEIBLER S, et al. From molecular to modular cellbiology[J]. Nature, 1999, 402:C47–C52.
[150] HAN J D J, BERTIN N, HAO T, et al. Evidence for dynamically organized modularityin the yeast protein-protein interaction network[J]. Nature, 2004, 430:88–93.
[151] STELLING J, SAUER U, SZALLASI Z, et al. Robustness of Cellular Functions[J]. Cell,2004, 118(6):675– 685.
[152] RAVASZ E, SOMERA A L, MONGRU D A, et al. Hierarchical organization of modularityin metabolic networks[J]. Science, 2002, 297:1551–1555.
[153] BARAB A′SI A L, RAVASZ E, VICSEK T. Deterministic Scale-Free Networks[J]. PhysicaA: Statistical Mechanics and its Applications, 2001, 299:559–564.
[154] DOROGOVTSEV S N, GOLTSEV A V, MENDES J F F. Pseudofractal scale-free web[J].Phys. Rev. E, 2002, 65(6):066122.
[155] NEWMAN M E J. Fast algorithm for detecting community structure in networks[J].Physical Review E, 2004, 69(6):066133.
[156] CLAUSET A, NEWMAN M E J, MOORE C. Finding community structure in very largenetworks[J]. Physical Review E, 2004, 70:066111.
[157]姚灿中,杨建梅.幂律拟合的进展及其在产业网络中的应用[J].管理学报, 5,2008:371–375.
[158] MANDELBROT B B, PASSOJA D E, PAULLAY A J. Fractal character of fracture surfacesof metals[J]. Nature, 1984, 308:721–722.
[159] STANLEY H E, MEAKIN P. Multifractal phenomena in physics and chemistry[J]. Na-ture, 1998, 335(6189):405–409.
[160] BROWN G, MICHON G, PEYRIE`RE J. On the multifractal analysis of measures[J].Journal of Statistical Physics, 1992, 66:775–790.
[161]李彤.多重分形原理及其若干应用[D].北京:北京交通大学, 2008.
[162] LEE C Y, JUNG S. Statistical self-similar properties of complex networks[J]. PhysicalReview E, 2006, 73(6):066102.
[163] GRASSBERGER P, PROCACCIA I. Characterization of Strange Attractors[J]. Phys. Rev.Lett., 1983, 50(5):346–349.
[164]左孝凌,李为鑑,刘永才.离散数学[M].上海:科学技术文献出版社, 1982.
[165]戴一奇,胡冠章,陈卫.图论与代数结构[M].北京:清华大学出版社, 2003.
[166] BU D, ZHAO Y, CAI L, et al. Topological Structure Analysis of the Protein-ProteinInteraction Network in Budding Yeast[J]. Nucleic Acids Research, 2003, 31(9):2443–2450.
[167] NEWMAN M E J. Assortative Mixing in Networks[J]. Phys. Rev. Lett., 2002,89(20):208701.
[168] PASTOR-SATORRAS R, V A′ZQUEZ A, VESPIGNANI A. Dynamical and CorrelationProperties of the Internet[J]. Phys. Rev. Lett., 2001, 87(25):258701.
[169] MASLOV S, SNEPPEN K. Specificity and Stability in Topology of Protein Networks[J].Science, 2002, 296(5569):910–913.
[170] NEWMAN M E J. Power laws, Pareto distributions and Zipf’s law[J]. ContemporaryPhysics, 2005, 46:323.
[171] WILLIS J C, YULE G U. Some statistics of evolution and geographical distribution inplants and animals, and their significance[J]. Nature, 1922, 109:177–179.
[172] ZANETTE D, MANRUBIA S. Vertical transmission of culture and the distribution offamily names[J]. Physica A: Statistical Mechanics and its Applications, 2001, 295(1-2):1– 8.
[173] BIANCONI G, BARAB A′SI A L. Bose-Einstein Condensation in Complex Networks[J].Physical Review Letters, 2001, 86(24):5632–5635.
[174] CHEN M J. Competitor Analysis and Interfirm Rivalry: Toward a Theoretical Integra-tion[J]. The Academy of Management Review, 1996, 21:100–134.
[175] MCGRATH R G, CHEN M J, MACMILLAN I C. Multimarket maneuvering in uncer-tain spheres of in?uence: Resource diversion strategies[J]. Academy of ManagementReview, 1998, 23:724–740.
[176] PORTER M E. Competitive Strategy: Techniques for Analyzing Industries and Com-petitors[M]. New York, USA: The Free Press, 1980.
[177] ZHUANG D, YANG J. Simulation of Rivalry Spread Effect over the CompetitivePressure Network[C]//Proceeding of the 2008 IEEE International Conference on Sys-tems, Man, and Cybernetics. Suntec Singapore: IEEE, 2008:851–855.
[178] NEWMAN M E J, GIRVAN M. Finding and evaluating community structure in net-works[J]. Physical Review E, 2004, 69:026113.
[179] PASTOR-SATORRAS R, VESPIGNANI A. Epidemic spreading in scale-free networks[J].Physical Review Letters, 2001, 86:3200–3203.
[180] HETHCOTE H. The Mathematics of Infectious Diseases[J]. SIAM Review, 2000,42:599–653.
[181] ZOU C C, TOWSLEY D, GONG W. Email Virus Propagation Modeling and Analysis[J].2003.
[182] LEONE M, VAZQUEZ A, VESPIGNANI A, et al. Ferromagnetic Ordering in Graphs withArbitrary Degree Distribution[J]. Eur. Physical J. B, 2002, 28(2):191–197.
[183] THILO G, HIROKI S. Adaptive Networks:Theory, Models and Applications[M]. Cam-bridge Massachusetts: Springer, 2009.
[2] BARAB A′SI A L, ALBERT R. Emergence of scaling in random networks[J]. Science,1999, 286:509–512.
[3]陈关荣.复杂网络及其新近研究进展简介[J].力学进展, 2008, 38(6):653–662.
[4] YANG J, LU L, XIE W, et al. On competitive relationship networks: A new method forindustrial competition analysis[J]. Physica A: Statistical Mechanics and its Applications,2007, 382(2):704– 714.
[5]杨建梅,陆履平,谢王丹.广州软件企业竞争关系的复杂网络分析[C]//第二届全国复杂动态网络学术论坛论文集.北京,中国:中国高等科学技术中心,2005:616–619.
[6] YANG J, WANG W, CHEN G. A two-level complex network model and its applica-tion[J]. Physica A: Statistical Mechanics and its Applications, 2009, 388(12):2435–2449.
[7] ZHUANG D, YANG J. Simulation of Rivalry Spread Effect over the Competitive Pres-sure Network[C]//Proceeding of the 2008 IEEE International Conference on Systems,Man, and Cybernetics. Suntec Singapore: IEEE, 2008:851–855.
[8]庄东.基于复杂网络的产业内厂商间竞争关系的建模与仿真[D].广州:华南理工大学, 2007.
[9]贝塔朗菲.一般系统论:基础、发展和应用[M].北京:清华大学出版社, 1987.
[10]戴汝为.复杂巨系统科学―一门21世纪的科学[J].自然杂志, 1997, 19 (4):187–192.
[11]霍兰J H.隐秩序-适应性造就复杂性[M].上海:上海科技教育出版社, 2001.
[12]于景元,涂元季.从定性到定量综合集成方法―案例研究[J].系统工程的理论与实践, 2002, 5:1–7.
[13]于景元,周晓纪.从定性到定量综合集成方法的实现和应用[J].系统工程理论与实践, 2002, 10:28–30.
[14]于景元.从综合集成方法思想到综合集成实践[J].管理学报, 2005, 1:4–10.
[15]汪小帆,李翔,陈关荣.复杂网络:理论及其应用[M].北京:清华大学出版社, 2006.
[16] WATTS D J, STROGATZ S H. Collective dynamics of’small-world’networks[J]. Nature,1998, 393:440–442.
[17] NEWMAN M E J, WATTS D J. Renormalization group analysis of the small-worldnetwork model[J]. Physics Letters A, 1999, 263(4-6):341– 346.
[18] DOROGOVTSEV S N, MENDES J F. Evolution of Networks[J]. Advances in Physics,2002, 51(4):1079–1187.
[19] KLEINBERG J M. Navigation in a small world[J]. Nature, 2001, 406:845.
[20] ALBERT R, BARAB A′SI A L. Topology of Evolving Networks: Local Events and Uni-versality[J]. Physical Review Letters, 2000, 85(24):5234–5237.
[21]郭雷,许晓鸣.复杂网络[M].上海:科技教育出版社, 2006.
[22] LUCE R. Connectivity and generalized n-cliques in sociometric group structure[J]. Psy-chometrika, 1950, 15:169–190.
[23] BRON C, KERBOSCH J. Finding all n-cliques of an undirected graph[J]. Comm of theACM, 16:575–577.
[24] TOMITA E, TANAKA A, TAKAHASHI H. The worst-case time complexity for generatingall maximal cliques and computational experiments[J]. Theoretical Computer Science,2006, 363 (1):28–42.
[25] TOMITA E, KAMEDA T. An efficient branch-and-bound algorithm for finding a maxi-mum clique with computational experiments[J]. Journal of Global Optimization, 2007,37 (1):95–111.
[26] BARAB A′SI A L, OLTVAI Z N. Network biology: understanding the cell’s functionalorganization[J]. Nature Reviews-Genetics, 2004, 5:101–114.
[27] MILO R, SHEN O S, ITZKOVITZ S, et al. Network motifs: Simpler building blocks ofcomplex networks[J]. Science, 2002, 298:824.
[28] SHEN O S, MILO R, MANGAN S, et al. Network motifs in the transcriptional regulationnetwork of Escherichia coli[J]. Nature Genetics, 2002, 31:64.
[29] SONG C, HAVLIN S, MAKSE H A. Origins of fractality in the growth of complexnetworks[J]. NATURE PHYSICS, 2006, 2:275.
[30] SONG C, HAVLIN S, MAKSE H A. Self-similarity of complex networks[J]. Nature,2005, 433:392.
[31] SONG C, GALLOS L K, HAVLIN S, et al. How to calculate the fractal dimension ofa complex network: the box covering algorithm[J]. Journal of Statistical Mechanics:Theory and Experiment, 2007, 2007(03):P03006.
[32] TAKEMOTO K, OOSAWA C, AKUTSU T. Structure of n-clique networks embeddedin a complex network[J]. Physica A: Statistical Mechanics and its Applications, 2007,380:665– 672.
[33] PALLA G, DERENYI I, FARKAS I, et al. Uncovering the overlapping community struc-ture of complex networks in nature and society[J]. Nature, 2005, 435:814–818.
[34] V A′ZQUEZ A, DOBRIN R, SERGI D, et al. The Topological Relationship between theLarge-Scale Attributes and Local Interaction Patterns of Complex Networks[J]. Pro-ceedings of the National Academy of Sciences of the United States of America, 2004,101(52):17940–17945.
[35] RAVASZ E, BARAB A′SI A L. Hierarchical organization in complex networks[J]. Phys.Rev. E, 2003, 67(2):026112.
[36] TAKEMOTO K, OOSAWA C. Evolving networks by merging cliques[J]. Phys. Rev. E,2005, 72(4):046116.
[37] PALLA G, BARABASI A L, VICSEK T. Quantifying social group evolution[J]. Nature,2007, 446:664–667.
[38] GOLTSEV A V, DOROGOVTSEV S N, MENDES J F F. ?? -core (bootstrap) percolationon complex networks: Critical phenomena and nonlocal effects[J]. Phys. Rev. E, 2006,73(5):056101.
[39] PETTIE S, RAMACHANDRAN V. An optimal minimum spanning tree algorithm[J]. J.ACM, 2002, 49(1):16–34.
[40] PETTIE S, RAMACHANDRAN V. A Randomized Time-Work Optimal Parallel Algo-rithm for Finding a Minimum Spanning Forest[J]. SIAM J. Comput., 2002, 31(6):1879–1895.
[41] BADER D A, CONG G. Fast shared-memory algorithms for computing the minimumspanning forest of sparse graphs[J]. J. Parallel Distrib. Comput., 2006, 66(11):1366–1378.
[42] GIBSON D, KLEINBERG J, RAGHAVAN P. Inferring Web communities from link topol-ogy[C]//Proceeding of the 9th ACM Conference on Hypertext and Hypermedia. NewYork, USA: ACM, 1998:225–234.
[43] FLAKE G W, LAWRENCE S R, GILES C L, et al. Self-organization and identificationof Web communities[J]. IEEE Computer, 2002, 35:66–71.
[44] ADAMIC L A, ADAR E. Friends and neighbors on the Web[J]. Social Networks, 2003,25(3):211–230.
[45] HOLME P, HUSS M, JEONG H. Subnetwork hierarchies of biochemical pathways[J].Bioinformatics, 2003, 19:532.
[46] WILKINSON D M, HUBERMAN B A. A method for finding communities of relatedgenes[J]. Proceedings of the National Academy of Sciences of the United States ofAmerica, 2004, 101(Suppl 1):5241–5248.
[47] GIRVAN M, NEWMAN M E J. Community structure in social and biological net-works[J]. Proc. Natl. Acad. Sci. USA, 2002, 99:7821–7826.
[48] GLEISER P, DANON L. Community structure in Jazz[J]. Advances in Complex Systems,2003, 6:565–573.
[49] NEWMAN M E J. Modularity and community structure in networks[J]. Proc. Natl.Acad. Sci. USA, 2006, 103:8577.
[50] NEWMAN M E J. Finding community structure in networks using the eigenvectors ofmatrices[J]. Physical Review E, 2006, 74:036104.
[51] NEWMAN M E J. Detecting community structure in networks[J]. The European PhysicalJournal B-Condensed Matter, 2004, 38:321–330.
[52] NEWMAN M E J. Fast algorithm for detecting community structure in networks[J].Physical Review E, 2004, 69:066133.
[53] LI X, CHEN G. A local-world evolving network model[J]. Physica A: Statistical Me-chanics and its Applications, 2003, 328(1-2):274– 286.
[54] LIU Z, LAI Y C, YE N, et al. Connectivity distribution and attack tolerance of generalnetworks with both preferential and random attachments[J]. Physics Letters A, 2002,303(5-6):337–344.
[55] RAMASCO J J, DOROGOVTSEV S N, PASTOR-SATORRAS R. Self-organization of col-laboration networks[J]. Phys. Rev. E, 2004, 70(3):036106.
[56] FAN Z, CHEN G, ZHANG Y. A comprehensive multi-local-world model for complexnetworks[J]. Physics Letters A, 2009, 373(18-19):1601–1605.
[57]方锦清,李永.网络科学中统一混合理论模型的若干研究进展[J].力学进展, 2008,38:663–678.
[58] ZHU C P, ZHOU T, YANG H J, et al. The process of coevolutionary competitive ex-clusion: speciation, multifractality and power-laws in correlations[J]. New Journal ofPhysics, 2008, 10(2):023006 (10pp).
[59] WU Z X, XU X J, WANG Y H. Maximal planar networks with large clustering coeffi-cient and power-law degree distribution[J]. Phys. Rev. E, 2006, 73(5):058101.
[60] WANG W X, WANG B H, HU B, et al. General Dynamics of Topology and Traffic onWeighted Technological Networks[J]. Phys. Rev. Lett., 2005, 94(18):188702.
[61] WANG W X, HU B, ZHOU T, et al. Mutual selection model for weighted networks[J].Phys. Rev. E, 2005, 72(4):046140.
[62] OU Q, JIN Y D, ZHOU T, et al. Power-law strength-degree correlation from resource-allocation dynamics on weighted networks[J]. Phys. Rev. E, 2007, 75(2):021102.
[63] ZHOU T, REN J, MEDO M C V, et al. Bipartite network projection and personal recom-mendation[J]. Phys. Rev. E, 2007, 76(4):046115.
[64] BARRAT A, BARTHE′LEMY M, VESPIGNANI A. Weighted Evolving Networks: Cou-pling Topology and Weight Dynamics[J]. Phys. Rev. Lett., 2004, 92(22):228701.
[65] FAN Y, LI M, CHEN J, et al. Network of Econophysicists: a weighted network to in-vestigate the development of Econophysics[J]. International Journal of Modern PhysicsB, 2004, 18:17–19.
[66] ZHANG P, LI M, WU J, et al. The analysis and dissimilarity comparison of communitystructure[J]. Physica A: Statistical Mechanics and its Applications, 2006, 367:577–585.
[67] FAN Y, LI M, ZHANG P, et al. Accuracy and precision of methods for communityidentification in weighted networks[J]. Physica A: Statistical Mechanics and its Appli-cations, 2007, 377(1):363– 372.
[68] LI M, FAN Y, WANG D, et al. Small-world effect induced by weight randomization onregular networks[J]. Physics Letters A, 2007, 364(6):488– 493.
[69] FAN Y, LI M, ZHANG P, et al. The effect of weight on community structure of net-works[J]. Physica A: Statistical Mechanics and its Applications, 2007, 378(2):583–590.
[70] LI M, WANG D, FAN Y, et al. Modelling weighted networks using connection count[J].New Journal of Physics, 2006, 8(5):72.
[71] LI M, WU J, WANG D, et al. Evolving model of weighted networks inspired by scien-tific collaboration networks[J]. Physica A: Statistical Mechanics and its Applications,2007, 375(1):355– 364.
[72] LIU Z, HU B. Epidemic spreading in community networks[J]. EPL (Europhysics Let-ters), 2005, 72(2):315–321.
[73] WU X, LIU Z. How community structure in?uences epidemic spread in social net-works[J]. Physica A: Statistical Mechanics and its Applications, 2008, 387(2-3):623–630.
[74] HUANG W, LI C. Epidemic spreading in scale-free networks with communitystructure[J]. Journal of Statistical Mechanics: Theory and Experiment, 2007,2007(01):P01014.
[75] ZHENG D F, HUI P, TRIMPER S, et al. Epidemics and dimensionality in hierarchicalnetworks[J]. Physica A: Statistical Mechanics and its Applications, 2005, 352(2-4):659– 668.
[76] ZHOU T, LIU J G, BAI W J, et al. Behaviors of susceptible-infected epidemics onscale-free networks with identical infectivity[J]. Phys. Rev. E, 2006, 74(5):056109.
[77] YANG R, WANG B H, REN J, et al. Epidemic spreading on heterogeneous networkswith identical infectivity[J]. Physics Letters A, 2007, 364(3-4):189– 193.
[78] YANG R, ZHOU T, XIE Y B, et al. Optimal contact process on complex networks[J].Phys. Rev. E, 2008, 78(6):066109.
[79] XU X J, WANG W X, ZHOU T, et al. Geographical effects on epidemic spreading inscale-free networks[J]. International Journal of Modern Physics C, 2006, 17:1815.
[80] XU X J, ZHANG X, MENDES J F F. Impacts of preference and geography on epidemicspreading[J]. Physical Review E, 2007, 76:056109.
[81] ZHOU J, LIU Z. Epidemic spreading in communities with mobile agents[J]. Physica A:Statistical Mechanics and its Applications, 2009, 388(7):1228– 1236.
[82] BAI W J, ZHOU T, WANG B H. Immunization of Susceptible-Infected Model on Scale-Free networks[J]. Physica A, 2007, 384:656–662.
[83] HAN X P. Disease spreading with epidemic alert on small-world networks[J]. PhysicsLetters A, 2007, 365(1-2):1–5.
[84] SMALL M, TSE C. Clustering model for transmission of the SARS virus: applicationto epidemic control and risk assessment[J]. Physica A: Statistical Mechanics and itsApplications, 2005, 351(2-4):499– 511.
[85] YAN G, ZHOU T, HU B, et al. Efficient routing on complex networks[J]. Phys. Rev. E,2006, 73(4):046108.
[86] MOTTER A E, ZHOU C, KURTHS J. Network synchronization, diffusion, and the para-dox of heterogeneity[J]. Phys. Rev. E, 2005, 71(1):016116.
[87] ZHOU C, MOTTER A E, KURTHS J. Universality in the Synchronization of WeightedRandom Networks[J]. Phys. Rev. Lett., 2006, 96(3):034101.
[88] ZHOU C, KURTHS J. Dynamical Weights and Enhanced Synchronization in AdaptiveComplex Networks[J]. Phys. Rev. Lett., 2006, 96(16):164102.
[89] WANG X, CHEN G. Synchronization in scale-free dynamical networks: robustness andfragility[J]. IEEE Trans. Circuits and Systems-I, 2002, 49:54–62.
[90] LI X, CHEN G R. Synchronization and desynchronization of complex dynamicalnetworks: an eigineering viewpoint[J]. IEEE Trans. Circuits and Systems-I, 2003,50:1381–1390.
[91] ZHAO M, ZHOU T, WANG B H, et al. Relations between average distance, heterogene-ity and network synchronizability[J]. Physica A: Statistical and Theoretical Physics,2006, 371(2):773– 780.
[92] XIANG W, BING-HONG W, TAO Z, et al. Synchronizability of Highly Clustered Scale-Free Networks[J]. Chinese Physics Letters, 2006, 23(4):1046–1049.
[93] ZHOU T, ZHAO M, CHEN G, et al. Phase synchronization on scale-free networks withcommunity structure[J]. Physics Letters A, 2007, 368(6):431– 434.
[94]吕金虎.复杂动力网络的数学模型与同步准则[J].系统工程理论与实践, 2004,4:17–22.
[95]吕金虎.复杂网络的同步:理论、方法、应用与展望[J].力学进展, 2008, 6:713–722.
[96] ZHAO M, ZHOU T, WANG B H, et al. Enhance synchronizability by structural pertur-bations[J]. Physical Review E, 2005, 72:057102.
[97] ZHAO M, ZHOU T, WANG B H, et al. Better synchronizability predicted by a newcoupling method[J]. The European Physical Journal B, 2006, 53:375.
[98] ZHOU T, ZHAO M, WANG B H. Better synchronizability predicted by crossed doublecycle[J]. Phys. Rev. E, 2006, 73(3):037101.
[99] WANG B, ZHOU T, XU Z L, et al. Optimizing synchronizability of networks[J]. Eur.Phys. J. B, 2007, 60:89–95.
[100] QIANG G, JIAN-GUO L, RUI-LI W, et al. Improvement of Synchronizability of Scale-Free Networks[J]. Chinese Physics Letters, 2007, 24(8):2437–2440.
[101] LI M, FAN Y, CHEN J, et al. Weighted networks of scientific communication: themeasurement and topological role of weight[J]. Physica A: Statistical Mechanics and itsApplications, 2005, 350(2-4):643– 656.
[102] ZHANG P P, CHEN K, HE Y, et al. Model and empirical study on some collaborationnetworks[J]. Physica A: Statistical Mechanics and its Applications, 2006, 360(2):599–616.
[103] CHANG H, SU B B, LIU C P, et al. Community, Hierarchy and Interweavement in Col-laboration Networks[J]. International Journal of Modern Physics C, 2008, 19(10):1537–1554.
[104]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.
[105] HU H, WANG X. Evolution of a large online social network[J]. Physics Letters A, 2009,373(12-13):1105– 1110.
[106] HU H B, WANG X F. Disassortative mixing in online social networks[J]. EurophysicsLetters, 2009, 86(1):18003.
[107] 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.
[108]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.
[109] CHEN Y Z, FU C H, CHANG H, et al. Connectivity correlations in three topologicalspaces of urban bus-transport networks in China[J]. Chin. Phys. B, 2008, 18:3580–3587.
[110] RU W, XU C. Hierarchical Structure, Disassortativity and Information Measures of theUS Flight Network[J]. Chinese Physics Letters, 2005, 22(10):2715–2718.
[111] 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).
[112] LIU J, DANG Y, WANG Z, et al. Relationship between the in-degree and out-degree ofWWW[J]. Physica. A, 2006, 371:861–869.
[113]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):3916–3921.
[114]胡鲜.基于复杂网络的中国汽车零部件企业竞争关系结构及行为研究[D].广州:华南理工大学, 2008.
[115]后锐,杨建梅,姚灿中.物流产业竞争关系的复杂网络模型研究[J].管理学报,2010, 7(3):1–6.
[116]刘浩.广州软件企业固话网络的增长机制研究[D].广州:华南理工大学, 2008.
[117]汤玮亮.百度百科的复杂网络建模与分析-大众生产视角[D].广州:华南理工大学, 2007.
[118]吴在伟.在线百科稳定性研究[D].广州:华南理工大学, 2009.
[119]潘向东.开源社区自组织演化问题研究[D].广州:华南理工大学, 2009.
[120] JIANMEI Y, HUANG X, ZHUANG D, et al. The Complex Network Analysis ofCompetitive Relationships Between Manufacturers in Foshan Ceramic Industry Clus-ter[C]//Proceedings of The 2006 International Conference on Management Science andEngineering (13th). Lille, France: Harbin Institute of Technology Press, 2006,II:1020–1023.
[121] TANG S H, YANG J, YAO C. Study on the Effect of Knowledge Diffusion on VirtualSocial-relationship Networks-Taking Book Inquiry as Example[C]//. Beijing: IEEE.Press, 2008:764–767.
[122]杨建梅,乐建兵.基于产业集群的企业重点投资地区决策的仿真[J].管理工程学报, 2005, 19(2):146–149.
[123]乐建兵,杨建梅,赵海霞.社会学仿真评述[J].科技管理研究, 2005, 12:263–267.
[124]乐建兵.基于多智能体仿真的广东产业集群成长机制研究[D].广州:华南理工大学, 2005.
[125]王铁,胡卫国.论中国汽车零部件产业组织政策[J].汽车工业研究, 2006, 11:6–12.
[126]王永祥,寇平均,楼志刚.我国汽车零部件产业的发展策略探讨[J].汽车工业研究, 2006, 2:20–22.
[127]李纪珍,贾永轩.汽车零部件整合[M].北京:机械工业出版社, 2006.
[128] HIPPEL E V, KROGH G V. Open Source Software and the”Private-Collective”Innova-tion Model: Issues for Organization Science[J]. Organization Science, 2003, 14(2):209–223.
[129]郭宇飚.知识经济中一种新的产权制度和生产方式――基于开源代码软件现象的研究[D].北京:北京大学, 2004.
[130] LERNER J, TIROLE J. Some Simple Economics of Open Source[J]. J.Indust.Econom.,2002, 50(2):1–55.
[131] DAVID P, BRADFORD C B.”Peer production”Promises to Leap in Importance[J].Information Week., 2002, 7:741.
[132] BENKLER Y. The Battle Over The Institutional Ecosystem in the Digital Environ-ment[J]. Communications of the ACM, 2002, 44(2):84–90.
[133] CORNEL J, KROWNE A. A Scholia - Based Document Model For Commons - BasedPeer Production[R]. Atlanta, USA: Proceedings of the Symposium on Free Culture andthe Digital, 2005.
[134] BENKLER Y. Coase’s penguin[J]. The Yale Law Journal, 2002, 112(3):369–446.
[135] BENKLER Y. Commons-based peer production and virture[J]. The Journal of PoliticalPhilosophy, 2006, 14(4):394–419.
[136] COASE R. The Nature of the Firm[J]. Economica, 1937, 4(16):386–405.
[137] WILLIAMSON O E, WINTER S G. The Nature of the Firm: Origins, Evolution, andDevelopment[M]. USA: Oxford University, 1993.
[138] TAPSCOTT D, WILLIAMS D, A. Wikinomics: How Mass Collaboration Changes Ev-erything[M]. New York: Portfolio Hardcover, 2007.
[139]王林,戴冠中.复杂网络的Scale-Free性、Scale-Free现象及其控制[M].北京:科学出版社, 2009.
[140] CLAUSET A, SHALIZI C R, NEWMAN M E J. Power-law distributions in empiricaldata[J]. SIAM Review, 2009, 51:661.
[141] GOLDSTEIN M L, MORRIS S A, YEN G G. Problems with fitting to the power-lawdistribution[J]. The European Physical Journal B - Condensed Matter and ComplexSystems, 2004, 41:255–258.
[142] SHALIZI C R. Maximum Likelihood Estimation for q-Exponential (Tsallis) Distribu-tions[J]. 2007.
[143] BAUKE H. Parameter estimation for power-law distributions by maximum likelihoodmethods[J]. The European Physical Journal B - Condensed Matter and Complex Sys-tems, 2007, 58:167–173.
[144] LAHERRE′RE J, SORNETTE D. Stretched exponential distributions in nature and econ-omy:“fat tails”with characteristic scales[J]. The European Physical Journal B - Con-densed Matter and Complex Systems, 1998, 2 2:525–539.
[145]王文杰.中国家电产业竞争关系复杂网络分析[D].广州:华南理工大学, 2006.
[146]汤玮亮.百度百科的复杂网络建模与分析-大众生产视角[D].广州:华南理工大学, 2007.
[147] DERE′NYI I, PALLA G, VICSEK T. Clique Percolation in Random Networks[J]. Phys.Rev. Lett., 2005, 94(16):160202.
[148] PALLA G, DERE′NYI I, FARKAS I, et al. Uncovering the overlapping community struc-ture of complex networks in nature and society[J]. Nature, 2005, 435:814–818.
[149] HARTWELL L H, HOPFIELD J J, LEIBLER S, et al. From molecular to modular cellbiology[J]. Nature, 1999, 402:C47–C52.
[150] HAN J D J, BERTIN N, HAO T, et al. Evidence for dynamically organized modularityin the yeast protein-protein interaction network[J]. Nature, 2004, 430:88–93.
[151] STELLING J, SAUER U, SZALLASI Z, et al. Robustness of Cellular Functions[J]. Cell,2004, 118(6):675– 685.
[152] RAVASZ E, SOMERA A L, MONGRU D A, et al. Hierarchical organization of modularityin metabolic networks[J]. Science, 2002, 297:1551–1555.
[153] BARAB A′SI A L, RAVASZ E, VICSEK T. Deterministic Scale-Free Networks[J]. PhysicaA: Statistical Mechanics and its Applications, 2001, 299:559–564.
[154] DOROGOVTSEV S N, GOLTSEV A V, MENDES J F F. Pseudofractal scale-free web[J].Phys. Rev. E, 2002, 65(6):066122.
[155] NEWMAN M E J. Fast algorithm for detecting community structure in networks[J].Physical Review E, 2004, 69(6):066133.
[156] CLAUSET A, NEWMAN M E J, MOORE C. Finding community structure in very largenetworks[J]. Physical Review E, 2004, 70:066111.
[157]姚灿中,杨建梅.幂律拟合的进展及其在产业网络中的应用[J].管理学报, 5,2008:371–375.
[158] MANDELBROT B B, PASSOJA D E, PAULLAY A J. Fractal character of fracture surfacesof metals[J]. Nature, 1984, 308:721–722.
[159] STANLEY H E, MEAKIN P. Multifractal phenomena in physics and chemistry[J]. Na-ture, 1998, 335(6189):405–409.
[160] BROWN G, MICHON G, PEYRIE`RE J. On the multifractal analysis of measures[J].Journal of Statistical Physics, 1992, 66:775–790.
[161]李彤.多重分形原理及其若干应用[D].北京:北京交通大学, 2008.
[162] LEE C Y, JUNG S. Statistical self-similar properties of complex networks[J]. PhysicalReview E, 2006, 73(6):066102.
[163] GRASSBERGER P, PROCACCIA I. Characterization of Strange Attractors[J]. Phys. Rev.Lett., 1983, 50(5):346–349.
[164]左孝凌,李为鑑,刘永才.离散数学[M].上海:科学技术文献出版社, 1982.
[165]戴一奇,胡冠章,陈卫.图论与代数结构[M].北京:清华大学出版社, 2003.
[166] BU D, ZHAO Y, CAI L, et al. Topological Structure Analysis of the Protein-ProteinInteraction Network in Budding Yeast[J]. Nucleic Acids Research, 2003, 31(9):2443–2450.
[167] NEWMAN M E J. Assortative Mixing in Networks[J]. Phys. Rev. Lett., 2002,89(20):208701.
[168] PASTOR-SATORRAS R, V A′ZQUEZ A, VESPIGNANI A. Dynamical and CorrelationProperties of the Internet[J]. Phys. Rev. Lett., 2001, 87(25):258701.
[169] MASLOV S, SNEPPEN K. Specificity and Stability in Topology of Protein Networks[J].Science, 2002, 296(5569):910–913.
[170] NEWMAN M E J. Power laws, Pareto distributions and Zipf’s law[J]. ContemporaryPhysics, 2005, 46:323.
[171] WILLIS J C, YULE G U. Some statistics of evolution and geographical distribution inplants and animals, and their significance[J]. Nature, 1922, 109:177–179.
[172] ZANETTE D, MANRUBIA S. Vertical transmission of culture and the distribution offamily names[J]. Physica A: Statistical Mechanics and its Applications, 2001, 295(1-2):1– 8.
[173] BIANCONI G, BARAB A′SI A L. Bose-Einstein Condensation in Complex Networks[J].Physical Review Letters, 2001, 86(24):5632–5635.
[174] CHEN M J. Competitor Analysis and Interfirm Rivalry: Toward a Theoretical Integra-tion[J]. The Academy of Management Review, 1996, 21:100–134.
[175] MCGRATH R G, CHEN M J, MACMILLAN I C. Multimarket maneuvering in uncer-tain spheres of in?uence: Resource diversion strategies[J]. Academy of ManagementReview, 1998, 23:724–740.
[176] PORTER M E. Competitive Strategy: Techniques for Analyzing Industries and Com-petitors[M]. New York, USA: The Free Press, 1980.
[177] ZHUANG D, YANG J. Simulation of Rivalry Spread Effect over the CompetitivePressure Network[C]//Proceeding of the 2008 IEEE International Conference on Sys-tems, Man, and Cybernetics. Suntec Singapore: IEEE, 2008:851–855.
[178] NEWMAN M E J, GIRVAN M. Finding and evaluating community structure in net-works[J]. Physical Review E, 2004, 69:026113.
[179] PASTOR-SATORRAS R, VESPIGNANI A. Epidemic spreading in scale-free networks[J].Physical Review Letters, 2001, 86:3200–3203.
[180] HETHCOTE H. The Mathematics of Infectious Diseases[J]. SIAM Review, 2000,42:599–653.
[181] ZOU C C, TOWSLEY D, GONG W. Email Virus Propagation Modeling and Analysis[J].2003.
[182] LEONE M, VAZQUEZ A, VESPIGNANI A, et al. Ferromagnetic Ordering in Graphs withArbitrary Degree Distribution[J]. Eur. Physical J. B, 2002, 28(2):191–197.
[183] THILO G, HIROKI S. Adaptive Networks:Theory, Models and Applications[M]. Cam-bridge Massachusetts: Springer, 2009.