复杂网络性质及传播动力学行为研究
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摘要
近十年来,复杂网络的研究取得了重要成果,主要体现在构建网络拓扑模型,分析网络性质,复杂网络上的传播动力学、复杂网络的同步与控制以及一些实证研究等方面。
本文在对复杂网络的概念和研究动态分析概括的基础上,讨论了数据挖掘与复杂网络研究的相关性,研究了可用于复杂网络分析的相关的数据挖掘算法：针对FP-TREE算法的序列发现效率问题,通过改进FP-TREE的结构,提出了一种具有较高挖掘效率的序列模式发现算法：在保证分类精度降低较少的前提下,通过在TSVM引入预测距离闽值,提出了一种提高分类效率的半监督学习方法；针对复杂网络社团发现算法中结点相似度度量问题,应用半监督学习及信息传播的思想,给出了结点相似性度量方法,定义了网络结点信息传播的两种方式：扩散传播与吸收传播方式,并证明了在这两种传播方式下结点的信息传播与结点信息向量表达之间的一致性及信息传播的收敛性,为复杂网络社团发现与数据挖掘聚类问题,提供了转化途径。
采用数据挖掘聚类算法对结点相似性度量方法进行验证,结果表明了该方法对社团划分的有效性；针对基于结点信息向量随着网络规模不断增加难以使用聚类算法完成对大规模网络划分社社团的问题,提出了一种基于单源信息传播的社团发现算法,并采用典型的测试网络验证了该算法的有效性。
对我国12座大中城市的公交线路网络的复杂性进行分析,采用基于单源信息传播社团发现算法完成了公交线路网络社团划分。
研究了多信息传播时,结点状态的复杂性,给出传播机制、作用机制和感染机制的定义,提出具有抑制作用的多信息传播模型SIn,并进行了仿真分析,结果与解析解较好吻合。
考虑网络拓扑结构对传播的影响,针对两种信息相互作用产生变异的情况,研究了异质网上的多信息传播过程,提出一种接触变异的传播模型—CM传播模型。分析了系统的相变情况,在不同传播率和变异率下信息传播动力学过程,社团结构对信息传播影响。
网络拓扑结构影响信息传播,信息传播也会影响网络的拓扑演化。通过分析信息传播过程与网络拓扑结构的随时间同步演化并相互作用,建立了一种基于网络结点状态的优先连接规则的动态增长网络模型,分析了该模型的拓扑性质。并研究了基于此模型的传播动力学行为。
In recent ten years, research of complex network has achieved a lot in many aspects, such as modeling topology of networks, analyzing character of networks, dynamics on networks, synchronization and control of networks and empirical study of networks.
With consideration of topology effecting information propagation, the relationship of data mining and complex network is discussed, and the relevant data mining algorithm is studied: through improving the structure of the FP-TREE, an algorithm of mining sequential patterns is proposed, which is the higher efficiency. Ensuring accuracy of classification, according to introducing TSVM distance threshold to predict, a semi-supervised learning method to improve the efficiency of classification is proposed. A new similarity method of nodes is proposed for community detection of complex networks. By transferring from topology similarity to vector similarity of nodes, community detection turns out to spatial data clustering. Two types of information propagation of nodes, diffusion and absorbing spreading, are defined. Consistency between information spreading and information vector of node and convergence of information spreading under these two types propagation are testified.
By adopting clustering algorithms in data mining for testifying method of information vector used in community detection, efficiency of this method is proved. For inefficiency of community detection in large networks by using information vector method mentioned above, a new algorithm based on single information spreading is proposed. Typical empirical networks are used to testify its validity.
Analyzing complexity of transportation networks in twelve cities of our country, community detection in those networks are archived by single information spreading mentioned above.
Complexity of node state is studied and mechanism of propagation and interaction and infection are defined when multi-information spreading. Multi-information propagation model Sln with inhibiting function is proposed. The results of this model are investigated analytically and by simulations.
Based on analyzing and summarizing concept and development of complex network, a variation spreading model caused by contact among of three messages and named CM model, is proposed, it has been analyzed that system transition, the dynamic process of information transmission with the different spreading rate and variation rate, and the effect with community structure.
Spreading of information affects the formation of topology of networks. By analyzing the coevolving and interaction between information propagation and formation of network topology, a dynamic growth network model is proposed. In the model, the links of a new node depends on the state and degree of nodes. On this model, dynamics of and on this network are studied.
本文在对复杂网络的概念和研究动态分析概括的基础上,讨论了数据挖掘与复杂网络研究的相关性,研究了可用于复杂网络分析的相关的数据挖掘算法：针对FP-TREE算法的序列发现效率问题,通过改进FP-TREE的结构,提出了一种具有较高挖掘效率的序列模式发现算法：在保证分类精度降低较少的前提下,通过在TSVM引入预测距离闽值,提出了一种提高分类效率的半监督学习方法；针对复杂网络社团发现算法中结点相似度度量问题,应用半监督学习及信息传播的思想,给出了结点相似性度量方法,定义了网络结点信息传播的两种方式：扩散传播与吸收传播方式,并证明了在这两种传播方式下结点的信息传播与结点信息向量表达之间的一致性及信息传播的收敛性,为复杂网络社团发现与数据挖掘聚类问题,提供了转化途径。
采用数据挖掘聚类算法对结点相似性度量方法进行验证,结果表明了该方法对社团划分的有效性；针对基于结点信息向量随着网络规模不断增加难以使用聚类算法完成对大规模网络划分社社团的问题,提出了一种基于单源信息传播的社团发现算法,并采用典型的测试网络验证了该算法的有效性。
对我国12座大中城市的公交线路网络的复杂性进行分析,采用基于单源信息传播社团发现算法完成了公交线路网络社团划分。
研究了多信息传播时,结点状态的复杂性,给出传播机制、作用机制和感染机制的定义,提出具有抑制作用的多信息传播模型SIn,并进行了仿真分析,结果与解析解较好吻合。
考虑网络拓扑结构对传播的影响,针对两种信息相互作用产生变异的情况,研究了异质网上的多信息传播过程,提出一种接触变异的传播模型—CM传播模型。分析了系统的相变情况,在不同传播率和变异率下信息传播动力学过程,社团结构对信息传播影响。
网络拓扑结构影响信息传播,信息传播也会影响网络的拓扑演化。通过分析信息传播过程与网络拓扑结构的随时间同步演化并相互作用,建立了一种基于网络结点状态的优先连接规则的动态增长网络模型,分析了该模型的拓扑性质。并研究了基于此模型的传播动力学行为。
In recent ten years, research of complex network has achieved a lot in many aspects, such as modeling topology of networks, analyzing character of networks, dynamics on networks, synchronization and control of networks and empirical study of networks.
With consideration of topology effecting information propagation, the relationship of data mining and complex network is discussed, and the relevant data mining algorithm is studied: through improving the structure of the FP-TREE, an algorithm of mining sequential patterns is proposed, which is the higher efficiency. Ensuring accuracy of classification, according to introducing TSVM distance threshold to predict, a semi-supervised learning method to improve the efficiency of classification is proposed. A new similarity method of nodes is proposed for community detection of complex networks. By transferring from topology similarity to vector similarity of nodes, community detection turns out to spatial data clustering. Two types of information propagation of nodes, diffusion and absorbing spreading, are defined. Consistency between information spreading and information vector of node and convergence of information spreading under these two types propagation are testified.
By adopting clustering algorithms in data mining for testifying method of information vector used in community detection, efficiency of this method is proved. For inefficiency of community detection in large networks by using information vector method mentioned above, a new algorithm based on single information spreading is proposed. Typical empirical networks are used to testify its validity.
Analyzing complexity of transportation networks in twelve cities of our country, community detection in those networks are archived by single information spreading mentioned above.
Complexity of node state is studied and mechanism of propagation and interaction and infection are defined when multi-information spreading. Multi-information propagation model Sln with inhibiting function is proposed. The results of this model are investigated analytically and by simulations.
Based on analyzing and summarizing concept and development of complex network, a variation spreading model caused by contact among of three messages and named CM model, is proposed, it has been analyzed that system transition, the dynamic process of information transmission with the different spreading rate and variation rate, and the effect with community structure.
Spreading of information affects the formation of topology of networks. By analyzing the coevolving and interaction between information propagation and formation of network topology, a dynamic growth network model is proposed. In the model, the links of a new node depends on the state and degree of nodes. On this model, dynamics of and on this network are studied.
引文
[1]Barabasi A L, Albert R. Emergence of scaling in random networks[J]. science, 1999,286:509-512.
[2]Krapivsky P L, Redner S. Organization of growing random networks[J]. Physical Review E,2001,63:66123.
[3]Dorogovtsev S N, Mendes J F F. Effect of the accelerating growth of communications networks on their structure[J]. Physical Review E,2001, 63:025101.
[4]Huberman B A, Adamic L A. Growth Dynamics of the World Wide Web[J]. Nature, 1999,401:131.
[5]Goh K I, Kahng B, Kim D. Fluctuation-driven dynamics of the Internet topology[J]. Physical Review Letters,2002,88:33.
[6]Ravasz E, Barabasi A L. Hierarchical organization in complex networks[J]. Physical Review E,2003,67:026112.
[7]Watts D J, Strogatz S H. Collective dynamics of 'small-world' networks[J]. Nature,1998,393:440-442.
[8]Pastor-Satorras R, Vespignani A. Epidemic spreading in scale-free networks[J]. Physical Review Letters,2001,86:3200-3203.
[9]Newman M E J, Watts D J. Scaling and percolation in the small-world network model[J]. Physical Review E,1999,60:7332-7342.
[10]Moukarzel C F. Spreading and shortest path in systems with long-range connections[J]. Physical Review E,1999,60:6263-6266.
[11]Newman M E J, Moore C, Watts D J. Mean-field solution of the small-world network model[J]. Physical Review Letters,2000,84:3201-3204.
[12]May R M, Lloyd A L. Infection dynamics on scale-free networks[J]. Physical Review E,2001,64:066112.
[13]Pastor-Satorras R, Vespignani A. Epidemic dynamics in finite size scale-free networks[J]. Physical Review E,2002,65:035108.
[14]Kuperman M, Abramson G. Small-world effect in an epidemiological model[J]. Physical Review Letters,2001,86(13):2909-2912.
[15]Zanette D H. Critical behavior of propagation on small-world networks[J]. Physical Review E,2001,64:050901.
[16]Boguna M, Pastor-satorras R, Vespignani A. Absence of epidemic threshold in scale-free networks with degree correlations[J]. Physical Review Letters,2003, 90:028701.
[17]夏承遗,刘忠信,陈增强,等.复杂网络上带有直接免疫的SIRS类传染模型研究[J].控制与决策,2008,23(4)：468-472.
[18]Liu Z H, Hu B. Epidemic spreading in community networks[J]. Euro-Physics Letters,2005,72(2):315-321.
[19]Huang W, Li C G. Epidemic spreading in scale-free networks with community structure[J]. Journal of Statistical Mechanics:Theory and Experiment, 2008(1):01014.
[20]Pastor-Satorras R, Vespignani A. Epidemic dynamics and endemic states in complex networks[J]. Physical Review E,2001,63:066117(1-8).
[21]Moreno Y, Pastor-Satorras R, Vespignani A. Epidemic outbreaks in complex heterogeneous networks[J]. The European Physical Journal B-Condensed Matter and Complex Systems,2002,26:521-529.
[22]Boguna M, Pastor-Satorras R, Vespignani A. Epidemic spreading.in complex networks with degree correlations[J]. Physics and Astronomy,2003, 625:127-147.
[23]Boguna M, Pastor-Satorras R. Epidemic spreading in correlated complex networks[J]. Physical Review E,2002,66:047104(1-4).
[24]Bailey N T J. The Mathematical Theory of Infectious Diseases and Its Applications[M]. New York:Hafner Press,1975.
[25]Anderson R M, May R M. Infectious Diseases in Humans[M]. Oxford:Oxford University Press,1992.
[26]Lloyd-Smith J 0, Schreiber S J, Lopp P E, Getz W M. Superspreading and the effect of individual variation on disease emergence[J]. Nature,2005, 438(7066):355-359.
[27]Galvani A P, May R M. Epidemiology:Dimensions of superspreading[J]. Nature, 2005,438(7066):293-295.
[28]Chu X W, Zhang Z Z, Guan J H, Zhou S G. Epidemic spreading with nonlinear infectivity in weighted scale-free networks[DB/OL].2009, arxiv:0903.0924vl.
[29]Colizza V, Pastor-Satorras R, Vespignani A. Reaction-diffusion processes and metapopulation models in heterogeneous networks[J]. Nature Physics,2007, 3:276-282.
[30]Baronchelli A, Catanzaro M, Pastor-Satorras R. Bosonic reaction-diffusion processes on scale-free networks[J]. Physical Review E,2008,78:016111.
[31]Zhou J, Liu Z H. Epidemic spreading in communities with mobile agents[J]. Physica A,2009,388:1228-1236.
[32]Zhou J, Liu Z H. Epidemic spreading in complex networks [J]. Frontiers of Physics in China,2008,3(3):331-348.
[33]Wu X Y, Liu Z H. How community structure influences epidemic spread in social networks[J]. Physica A,2008,387:623-630.
[34]Tang M, Liu L, Liu Z H. Influence of dynamical condensation on epidemic spreading in scale-free networks[J]. Physical Review E,2009,79:016108.
[35]Zhou Y Z, Liu Z H, Zhou J. Periodic wave of epidemic Spreading in community Networks[J]. Chinese Physics Letters,2007,24(2):581-584.
[36]Ball F, sirl D, Trapman P. Threshold behavior and final outcome of an epidemic on a random network with household structure[J]. Advances in Applied Probability 2009,41(3):765-796.
[37]Nekovee M, Moreno Y, Bianconi G, Marsili M. Theory of rumor spreading in complex social networks[J]. Physica A:Statistical Mechanics and its Applications, 2007,374(1):457-470.
[38]Barthelemy M, Barrat A, Pastor-Satorras R, Vespignani A. Velocity and hierarchical spread of epidemic outbreaks in scale-free networks[J]. Physical Review Letters,2004,92(17):178701.
[39]Xia C Y, Liu Z X, Chen Z Q, et al. Dynamic spreading behavior of homogeneous and heterogeneous networks[J]. Progress in Natural Science,2007, 17(3):358-365.
[40]Xia C Y, Liu Z X, Chen Z Q, et al. Epidemic spreading behavior on local-world evolving networks[J]. Progress in Natural Science,2008,18(6):653-658.
[41]Xia C Y, Liu Z X, Chen Z Q, et al. A new multistage epidemiological model on complex networks[J]. Dynamics of Continuous, Discrete, and Impulsive Systems-Series B,2007,14(S6):160-165.
[42]Zheng D F, Hu P M, Trimper S. Epidemics and dimensionality in hierarchical networks[J]. Physica A,2005,352:659-668.
[43]Li X, Wang X F. Controlling the spreading in small-world evolving networks: stability, oscillation, and topology[C]. IEEE Transactions on Automatic Control,2006,51 (3):534-540.
[44]Gross T, D'Lima C J D, Blasius B. Epidemic dynamics in an adaptive networks [J]. Physical Review Letters,2006,96:208701.
[45]Xu X J, Zhang X, Mendes J F F. Impacts of preference and geography on epidemic spreading[J]. Physical Review E,2007,76:056109.
[46]Karrer B, Newman M E J. A message passing approach for general epidemic models[DB/OL].2010, arXiv:1003.5673v1.
[47]Eguiluz V M, Klemm K. Epidemic threshold in structured scale-free networks[J]. Physical Review Letters, 2002,89(10):108701.
[48]Y. Moreno, J. B. Gomez, Pacheco A F. Epidemic incidence in correlated complex networks[J]. Physical Review E,2003,68(3):035103.
[49]Joo J, Lebowitz J L. Behavior of susceptible-infected-susceptible epidemics on heterogeneous networks with saturation[J]. Physical Review E,2004, 69(6):066105.
[50]Grabowski A, Kosinski R A. Epidemic spreading in a hierarchical social network[J]. Physical Review E,2004,70(3):031908.
[51]Xu X J, Wang W X, Zhou T, Chen G. Geographical effects on epidemic spreading in scale-free networks[J]. Computational Physics and Physical Computation, 2006,17(12):1815-1822.
[52]许丹,李翔,汪小帆.局域世界复杂网络中的病毒传播及其免疫控制[J].控制与决策,2006,21(7)：817-820.
[53]许田,张培培,姜玉梅,苏蓓蓓,何大韧.流行病传播模型与SARS[J].自然杂志,2003,26(1)：20-25.
[54]杨洪勇,张嗣赢.基于复杂网络的禽流感病毒传播[J].系统仿真学报,2008,20(18)：5001-5005.
[55]Bai W J, Zhou T, Wang B H. Interplay between HIV/AIDS epidemics and demographic structures based on sexual contact networks[DB/OL].2006, arxiv:0602137.
[56]Han X P, Wang B H, Zhou C S, Zhou T, Zhu J F. Scaling in the Global Spreading Patterns of Pandemic Influenza A and the Role of Control:Empirical Statistics and Modeling[DB/OL].2009, arXiv:0912.1390.
[57]Barabasi A L, Albert R, Jeong H. Mean-field theory for scale-free random networks[J]. Physica A,1999,272:173-187.
[58]吴建军.城市交通网络拓扑结构复杂性研究[D].北京交通大学,2008,P20-21.
[59]Watts D J. Small Worlds:The dynamics of networks between order and randomness[M]. Princeton University Press,1999.
[60]Newman M E J, Girvan M. Finding and evaluating community structure in networks[J]. Physical Review E,2004,69:026113.
[61]Newman M E J. Scientific collaboration networks:Ⅱ. Shortest paths, weighted networks, and centrality[J]. Physical Review E,2001,64:016132.
[62]Newman M E J. The structure and function of complex networks[J]. SIAM Review,2003, 45:167-256.
[63]Newman M E J. Scientific collaboration networks. I. Network construction and fundamental results[J]. Physical Review E,2001,64:016131.
[64]Barrat A, Weigt M. On the properties of small world networks [J]. The European Physical Journal B,2000,13:547-560.
[65]Alon N, Yuster R, Zwick U. Finding and counting given length cycles[J]. Algorithmica,1997,17:209-223.
[66]李晓佳,张鹏,狄增如,樊瑛.复杂网络中的社团结构[J].复杂系统与复杂性科学,2008,5(3)：19-42.
[67]Newman M E J, Watts D J. Renormalization group analysis of the small-world network model[J]. Physical Letters A,1999,263:341-346.
[68]Newman M E J. The structure and function of networks[J]. Computer Physics Communication,2002,147:40-45.
[69]Liu Z H, et al. Connective distribution and attack tolerance of general networks with both preferential and random attachments[J]. Physics Letters A,2002, 303:337-344.
[70]Shi D H, Chen Q H, Liu L M. Markov chain-based numerical method for degree distribution of growing networks[J]. Physical Review E,2005,71:036140.
[71]Bollobas B, Riordan 0. Mathematical results on scale-free random graphs[M]. In:Bornholdt, S, Schuster H G(ed.) Handbook of Graphs and Networks:From the Genome to the Internet, Berlin:Wiley-VCH,2003,1-34.
[72]Cohen R, Havlin S. Scale-free networks are ultra small[J]. Physical Review Letters,2003,90:058701.
[73]Krapivsky P L, Redner S, Leyvraz F. Connectivity of growing random networks[J]. Physical Review Letters,2000,85:4629-4632.
[74]Dorogovtsev S N, Mendes J F F, Samukhin A N. Structure of growth networks with preferential linking[J]. Physical Review Letters.2000,85:4633-4636.
[75]Fronczak A, Fronczak P, and Holyst J A. Mean-field theory for clustering coefficients in Barabasi-Albert networks[J]. Physical Review E 64,2001, 026118.
[76]邵峰晶,于忠清,王金龙,孙仁诚.数据挖掘原理与算法(第二版)[M].北京：科学出版社,2009.8.
[77]Agrawal R, Imielinski T, Swami A. Mining Associations between Sets of Items in Massive Databases[C]. Process of the ACM-SIGMOD 1993 Int'1 Conference on Management of Data, Washington D.C., May 1993.
[78]Han J W, Pei J. FreeSpan:Frequent pattern projected sequential pattern mining[C]. International Conference on Knowledge Discovery and Data Mining, Proceedings of the sixth ACM SIGKDD international conference on Knowledge discovery and data mining, Boston:MAACM Press,2000,355-359.
[79]Han J W, Pei J. PrefixSpan:Mining sequential patterns efficiently by prefix-projected pattern growth[C]. IEEE Transactions on Knowledge and Data Engineering,2004,1-17.
[80]Han J W, Pei J, Yin Y W. Mining frequent patterns without candidate generation[C]. Proceedings of ACM SIGMOD Intl. Conference on Management of Data, Dallas:ACM Press,2000,1-12.
[81]Agrawal R, Srikant R. Mining sequential patterns:Generalization and performance improvement[C]. In:Proc of the 5th International Conference on Extending Database Technology (EDB T96). Berlin:Springer Verlag,1996,3-17.
[82]mannila H, Toivonen H, Verkamo A I. Discovery of frequent episodes in event sequences[J]. Data Mining and Knowledge Discovery,1997,1:259-289.
[83]Agrawal R, Srikant R. Mining quantitative association rules in large relational tables[C]. In proc.1996 ACM-SIGMOD Int. Conf. Management of Data, pages, Montreal, Canada,1996.6,1-12.
[84]Zaki M J. SPADE:An efficient algorithm for mining frequent sequences[J]. Machine Learning,2001,42(1-2):31-60.
[85]Shao F J, Sun R C, Yu Z Q. An Outlier-analysis algorithm based on the reduction of boundary cells influence[C]. Proc. Of the 8th Joint International Computer Conference,2002,536-540.
[86]高俊,施伯乐.快速关联规则挖掘算法研究[J].计算机科学,2005,32(3)：200-201.
[87]Li Y C, Chang C C. A new FP-tree algorithm for mining frequent itemsets[C]. AWCC 2004. LNCS 3309,2004,26-277.
[88]Han J, Pei J, Yin Y, Mao R. Mining frequent patterns without candidate generation:A Frequent pattern tree approach[J]. Data Mining and knowledge Discovery,2004.8,53-87.444.
[89]Bennett K P. Combining support vector and mathematical programming methods for classification. Advances in kernel methods:support vector learning[M], MIT Press,1999, P307-326.
[90]Vapnik V. Statistical learning theory[M]. New York:Wiley,1998.
[91]Gunn S R. Support vector machines for classification and regression[C]. ISIS Technical Report,1998.
[92]Gibson D, Kleinberg J M K, Raghavan P. Inferring web communities from link topology[C]. In Proceedings of the 9th ACM Conference on Hypertext and Hypermedia, Association of Computing Machinery, New York,1998.
[93]Flake G W, Lawrence S, Giles C L, Coetzee F M. Self-Organization and identification of Web communities[J]. IEEE Computer,2002,35(3):66-71.
[94]Guimera R, Amaral L A N. Functional cartography of complex metabolic networks[J]. Nature,2005,433(7028):895-900.
[95]Wu J J, Gao Z Y, Sun H J. Cascade and breakdown in scale-free networks with community structure[J]. Physical review E, Statistical, nonlinear, and soft matter physics,2006,74(6 Pt 2):066111.
[96]Leon D, Alex A, Albert D G. Impact of community structure on information transfer[J]. Physical review. E, Statistical, nonlinear, and soft matter physics,2008,77(3 Pt 2):036103.
[97]Girvan M, Newman M E J. Community structure in social and biological networks[C]. Proc. of the National Academy of Science,2002,9(12):7821-7826.
[98]Tyler J R, Wilkinson D M, Huberman B A. Email as spectroscopy:Automated discovery of community structure within organizations[C]. In:Huysman M, Wenger E, Wulf V, eds. Proc. of the 1st Int'1 Conf. on Communities and Technologies. Dordrecht:Kluwer Academic Publishers,2003,81-96.
[99]Palla G, Derenyi I, Farkas I, Vicsek T. Uncovering the overlapping community structure of complex networks in nature and society[J]. Nature,2005, 435(7043):814-818.
[100]Ravasz E, Somera A L, Mongru D A. Hierarchical organization of modularity in metabolic networks[J]. Science,2002,297(5586):1551-1555.
[101]Wang Z, Zhang J. In search of the biological significance of modular structures in protein networks[J]. PLOS Computational Biology,2007,3(6):107.
[102]Spirin V, Mirny L A. Protein complexes and functional modules in molecular networks[C]. Proc. of the National Academy of Science,2003, 100(21):12123-12128.
[103]Li X, Liu B, Yu PS. Discovering overlapping communities of named entities[C]. In:Furnkranz J, Scheffer T, Spiliopoulou M, eds. Proc. of the 10th European Conf. on Principles and Practice of Knowledge Discovery in Databases. Berlin: Springer-Verlag,2006,593-600.
[104]Ino H, Kudo M, Nakamura A. Partitioning of Web graphs by community topology[C]. In:Ellis A, Hagino T, eds. Proc. of the 14th Int'1 Conf. on World Wide Web. New York:ACM Press,2005,661-669.
[105]Sidiropoulos A, Pallis G, Katsaros D, Stamos K, Vakali A, Manolopoulos Y. Prefetching in content distribution networks via Web communities identification and outsourcing[J]. World Wide Web,2008,11(1):39-70.
[106]Almeida R B, Almeida V A F. A community-aware search engine[C]. In:Feldman SI, Uretsky M, Najork M, Wills CE, eds. Proc. of the 13th Int'1 Conf. on World Wide Web. New York:ACM Press,2004,413-421.
[107]Ghosh R, Lerman K. Community detection using a measure of global influence[C]. In Proceedings of KDD workshop on Social Network Analysis (SNAKDD),2008, eprint arXiv:0805.4606.
[108]Arenas A, Duch J, Fernandez A, Gomez S. Size reduction of complex networks preserving modularity[J]. New Journal of Physics,2007,9:176.
[109]Leicht E A, Newman M E J. Community structure in directed networks [J]. Physical Review Letters,2008,100(11):118703.
[110]Santo F. Community detection in graphs[J]. Physics Reports,2010, 486(3-5):75-174.
[111]Burt R S. Positions in networks[J]. Soc. Forces,1976,55:93.
[112]Wasserman S, Faust K. Social network analysis[M]. Cambridge University Press, Cambridge, UK.1994.
[113]Fouss F, Renders J M. Random-walk computation of similarities between nodes of a graph with application to collaborative recommendation[J]. IEEE Trans. on Knowledge and Data Eng. member-Pirotte, Alain and Member-Saerens, Marco. 2007,19(3):355.
[114]Saerens M, Fouss F, Yen L, Dupont P. The Principal Components Analysis of a Graph and its Relationships to Spectral Clustering[C]. Proceedings of the 15th European Conference on Machine Learning (ECML 2004). Lecture Notes in Artificial Intelligence, Pisa, Italy,2004, p371-383.
[115]Yen L, Fouss F, Decaestecker C, Francq P, Saerens M. Graph Nodes Clustering Based on the Commute-Time Kernel[C]. In PAKDD,2007, P1037-1045.
[116]Yen L, Fouss F, Decaestecker C, Francq P, Saerens M. Graph nodes clustering with the sigmoid commute-time kernel:A comparative study [J]. Data & Knowledge Engineering,2009,68(3):338-361.
[117]Zhou H. Distance, dissimilarity index, and network community structure[J]. Physal Review E,2003,67(6):061901.
[118]Palmer C R, Faloutsos C. Electricity Based External Similarity of Categorical Attributes[C]. In Proceedings of PAKDD,2003, P486-500.
[119]Tong H, Faloutsos C, Pan J Y. Random walk with restart:fast solutions and applications[J]. Knowledge and Information Systems,2008,14(3):327-346.
[120]Gori M, Pucci A. ItemRank:A random-walk based scoring algorithm for recommender engines[C]. In IJCAI'07:Proceedings of the 20th international joint conference on Artificial intelligence,2007,2766-2771.
[121]Brin S, Page L. The anatomy of a large-scale hypertextual Web search engine [J]. Computer Networks and ISDN Systems,1998,30(1-7):107.
[122]Estrada E, Hatano N. Communicability in complex networks[J]. Physical Review E,2008,77(3):036111.
[123]Estrada E, Hatano N. Communicability graph and community structures in complex networks[J]. Applied Mathematics and Computation,2009,214(2):500-511.
[124]Zhu X J. Semi-Supervised Learning with Graphs [D]. Carnegie Mellon University, CMU-LTI-05-192,2005.
[125]Donath W, Hoffman A. Lower bounds for the partitioning of graphs [J]. IBM Journal of Research and Development,1973,17(5):420.
[126]Fiedler M. Algebraic connectivity of graphs[J]. Czechoslovak Mathematical Journal,1973,23 (98):298-305.
[127]Spielman D A, Teng S H. Spectral Partitioning Works:Planar Graphs and Finite Element Meshes[C]. IEEE Symposium on Foundation of Computer Science,1996, 96-105.
[128]Fortunato S. Community detection in graphs[DB/OL]. arXiv:0906.0612v2,2009.6.
[129]Kernighan B W, Lin S. An efficient heuristic procedure for partitioning graphs[J]. Bell System Technical Journal,1970,49:291-307.
[130]Newman M E J, Girvan M. Detecting community structure in networks[J], The European Physical Journal B,2004,38:321-330.
[131]Radicchi F, Castellano C, Cecconi F, et al. Defining and identifying communities in networks [J]. Proceedings of the National Academy Sciences of the USA,2004, 101(9):2658-2663.
[132]Latora V, Marchion M. Efficient behavior of small-world networks [J]. Physical Review Letters,2001,87(19):198701.
[133]Latora V, Marchiori M. Economic small-world behavior in weighted networks[J]. The European Physical Journal B,2003,32:249-263.
[134]Latora V, Marchiori M. A measure of centrality based on the network efficiency[J]. New Journal of Physics,2007,9:188.
[135]Fortunato S, Latora V, Marchiori M. Method to find community structures based on information centrality[J]. Physical review E,2004,70(5):056104.
[136]Hastie T, Tibshirani R, Friedman J H. The Elements of Statistical Learning[M]. Springer, Berlin, Germany, ISBN 0387952845 2001.
[137]汪小帆,刘亚冰.复杂网络中的社团结构算法综述[J].电子科技大学学报,2009(9),38(5)：537-543.
[138]Zachary W W. An information flow mode1 for conflict and fission in small groups[J]. Journal of Anthropological Research,1977,33(4):452-473.
[139]Pang C J, Shao F J, Sun R C. Detecting Community Structure in Networks by Propagating Labels of Nodes[C]. Sixth International Symposium on Neural Networks, ISNN2009, WuHan, China. (ISSN2009).2009.5.839-846.
[140]Mendes J F F, Dorogovtsev S N, and Ioffe A F. Evolution of networks:From Biological Nets to the Internet and WWW[M]. Oxford:Oxford University Press, 2003.
[141]Latora V, Marchiori M. Is the Boston subway a smallworld network? [J] Physica A,2002,314:109-113.
[142]Sen P, Dasgupta S, Chatterjee A. Small-world properties of the Indian railway network[J]. Physical Review E,2003,67:036106.
[143]Seaton K A, Hackett L M. Stations, trains and small-world networks [J]. Physica A,2004,339:635-644.
[144]Jiang B, Claramunt C. Topological analysis of urban street networks[J]. Environment and Planning B,2004,31:151-162.
[145]Li W, Cai X. Statistical analysis of airport network of China[J]. Physical Review E,2003,69:046106.
[146]Guimera R, Mossa S, Turtschi A, Amaral L A N. The worldwide air transportation network:Anomalous centrality,community structure, and cities' global roles[J]. PNAS,2005,102:7794-7799.
[147]Wu J J, Gao Z Y, Sun Huijun. Urban transit system as a scale-free network[J]. Modern Physics Letters B,2004,18:1043-1049.
[148]Lu H P, Shi Y. Complexity of Public Transport Networks[J]. TSINGHUA SCIENCE AND TECHNOLOGY.2007,12(2):204-213.
[149]Xu X P, Hu J H, Liu F, Liu L S. Scaling and correlations in three bus-transport networks of China[J]. Physical A,2007,374:441.
[150]常鸣,马寿峰.我国大城市公交网络结构的实证研究[J].系统工程学报.2007,22(04)：412-418.
[151]Sun R C, Shao F J. Analysis of Qingdao's Public Transport Line Network[C]. 2008 IEEE International Conference on Automation and Logistics (ICAL 2008), 2008.9,1147-1150.
[152]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.
[153]王喆, 彭其渊.成都市公交复杂网络拓扑特性研究[J].交通与计算机,2007,25(2)：39-42.
[154]李英,周伟,郭世进.上海公共交通网络复杂性分析[J].系统工程,2007,25(1)：38-41.
[155]张晨,张宁.上海市公交网络拓扑性质研究[J].上海理工大学学报,2006,28(5)：489-494.
[156]冷静.青岛城市空间结构的变迁与发展[N].青岛日报,2009.9.1.
[157]Hethcote H W. The mathematics of infectious diseases[J]. SIAM Review,2000, 42(4):599-653.
[158]郭雷,许晓鸣 主编.复杂网络[M].上海：上海科技教育出版社,2006：115-140.
[159]Das Bistro Project's anti-code-red default.ida. http://www.dasbitro.com/default.ida.
[160]Liljenstam M, Nicol D. Comparing passive and active worm defenses[C]. Proceedings of the 1st International Conference on Quantitative Evaluation of Systems (QEST),2004 September.
[161]Nicol D, Liljenstam M. Models of active worm defenses[C]. Proceedings of the IPSI Studenica Conference,2004 June.
[162]杨峰,段海新,李星.网络蠕虫扩散中蠕虫和良性蠕虫交互过程建模与分析[J].中国科学E辑信息科学,2004,34(8)：841-856.
[163]Newman M E J. Threshold effects for two pathogens spreading on a network[J]. Physical Review Letters,2005,95:108701.
[164]Ahn Y Y, Masuda N, Jeong H, Noh J D. Epidemic dynamics of Interacting two particle species on scale-free networks[J]. Physical Review E,2006, 74(6):066113.
[165]Moore C, Newman M E J. Epidemics and percolation in small-world networks [J]. Physical Review E,2000,61:5678-5682.
[166]Moore C, Newman M E J. Exact solution of site and bond percolation on small-world networks[J]. Physical Review E,2000,62:7059-7064.
[167]Newman M E J, Jensen I, Ziff R M. Percolation and epidemics in a two-dimensional small world[J]. Physical Review E,2002,65:021904.
[168]Abramson G. Kuperman M, Social games in a social network[J]. Physical Review E,2001,63(3):030901.
[169]Agiza H N, Elgazzar A S, Youssef S A. Phase transitions in some epidemic models defined on small-world networks[DB/OL].2003, arXiv:0301004.
[170]周涛,傅忠谦,牛永伟,王达,曾燕,汀秉宏,周佩玲.复杂网络上传播动力学研究综述[J].自然科学进展,2005,15(5)：513-518.
[171]Pastor-Satorras R. and Vespignani A. Epidemics and immunization in scale-free networks[M]. In:Bornholdt S, Schuster HG(eds.) Handbook of Graph and Networks. Berlin:Wiley-VCH,2003.
[172]Barabasi A L, Albert R, and Jeong H. Scale-free characteristics of random networks:the topology of the world-wide web[J]. Physica A,2000,281:69-77.
[173]Price D J. Networks of scientific papers [J]. Science,1965,149:510-515.
[174]Gross T, Blasius B. Adaptive coevolutionary networks:a review[J]. Journal of the royal society interface,2008,5:259-271.
[175]Gross T, Kevrekidis I G. Coarse-graining adaptive coevolutionary network dynamics via automated moment closure[DB/OL].2007, arXiv:0702047.
[176]Ehrhardt, George C M A, Marsili M. Vega-Redondo F. Phenomenological models of socio-economic network dynamics[J]. Physical Review E,2006,74:036106-11.
[177]Zanette D. Coevolution of agents and networks in an epidemiological model [DB/OL].2007, arXiv:0707.
[178]Zanette D H, Gil S. Opinion spreading and agent segregation on evolving networks [J]. Physica D,2006,224:156-165.
[179]Gil S, Zanette D H. Coevolution of agents and networks:opinion spreading and community disconnection[J]. Physical Letters A,2006,356:89-95.
[180]Holme P, Newman M E J. Nonequilibrium phase transition in the coevolution of networks and opinions[J]. Physical Review E,2007,74:056108-5.
[181]Keeling M J, Rand D A, Morris A J. Correlation models for childhood epidemics[J]. Proceedings the Royal Society B,1995,264:1149-1156.
[182]Holme P, Kim B J. Growing scale-free networks with tunable clustering[J]. Physical Review E,2002,65:026107.
[183]Tian L, Zhu C P, Shi D N, Gu Z M. Universal scaling behavior of clustering coefficient induced by deactivation mechanism[J]. Physical Review E,2006, 74:046103.
[184]Volz E, Meyers L A. Susceptible-infected-recovered epidemics in dynamic contact networks[C]. Proceedings of the Royal Society B:Biological Sciences, 2007,274(1628):2925-2933.
[185]Fefferman N H, Ng K L. How disease models in static networks can fail to approximate disease in dynamic networks[J]. Physical Review E,2007, 76:031919.
[186]Shaw L B, Schwartz I B. Rewiring for adaptation[J]. Physics,2010,3.17.
[187]Shaw L B, Schwartz I B. In Adaptive Networks:Theory, Models and Applications, edited by T[DB/OL]. Gross and H. Sayama (Springer/NECSI,2009), Studies on Complexity Series.
[188]Boguna M, Pastor-satorras R, Vespignani A. Stochastic theory of synchronization transitions in extended systems[J]. Physical Review Letters, 2003,90(20):204101.
[189]Sienkiewicz J, Holyst J A. Statistical analysis of 22 public transport networks in Poland[J].2005, arxiv:0506074.
[190]Ferber C V, Holovatch Y, Palchykov V. Scaling in publictransport networks [J]. 2005, arxiv:0501296.
[2]Krapivsky P L, Redner S. Organization of growing random networks[J]. Physical Review E,2001,63:66123.
[3]Dorogovtsev S N, Mendes J F F. Effect of the accelerating growth of communications networks on their structure[J]. Physical Review E,2001, 63:025101.
[4]Huberman B A, Adamic L A. Growth Dynamics of the World Wide Web[J]. Nature, 1999,401:131.
[5]Goh K I, Kahng B, Kim D. Fluctuation-driven dynamics of the Internet topology[J]. Physical Review Letters,2002,88:33.
[6]Ravasz E, Barabasi A L. Hierarchical organization in complex networks[J]. Physical Review E,2003,67:026112.
[7]Watts D J, Strogatz S H. Collective dynamics of 'small-world' networks[J]. Nature,1998,393:440-442.
[8]Pastor-Satorras R, Vespignani A. Epidemic spreading in scale-free networks[J]. Physical Review Letters,2001,86:3200-3203.
[9]Newman M E J, Watts D J. Scaling and percolation in the small-world network model[J]. Physical Review E,1999,60:7332-7342.
[10]Moukarzel C F. Spreading and shortest path in systems with long-range connections[J]. Physical Review E,1999,60:6263-6266.
[11]Newman M E J, Moore C, Watts D J. Mean-field solution of the small-world network model[J]. Physical Review Letters,2000,84:3201-3204.
[12]May R M, Lloyd A L. Infection dynamics on scale-free networks[J]. Physical Review E,2001,64:066112.
[13]Pastor-Satorras R, Vespignani A. Epidemic dynamics in finite size scale-free networks[J]. Physical Review E,2002,65:035108.
[14]Kuperman M, Abramson G. Small-world effect in an epidemiological model[J]. Physical Review Letters,2001,86(13):2909-2912.
[15]Zanette D H. Critical behavior of propagation on small-world networks[J]. Physical Review E,2001,64:050901.
[16]Boguna M, Pastor-satorras R, Vespignani A. Absence of epidemic threshold in scale-free networks with degree correlations[J]. Physical Review Letters,2003, 90:028701.
[17]夏承遗,刘忠信,陈增强,等.复杂网络上带有直接免疫的SIRS类传染模型研究[J].控制与决策,2008,23(4)：468-472.
[18]Liu Z H, Hu B. Epidemic spreading in community networks[J]. Euro-Physics Letters,2005,72(2):315-321.
[19]Huang W, Li C G. Epidemic spreading in scale-free networks with community structure[J]. Journal of Statistical Mechanics:Theory and Experiment, 2008(1):01014.
[20]Pastor-Satorras R, Vespignani A. Epidemic dynamics and endemic states in complex networks[J]. Physical Review E,2001,63:066117(1-8).
[21]Moreno Y, Pastor-Satorras R, Vespignani A. Epidemic outbreaks in complex heterogeneous networks[J]. The European Physical Journal B-Condensed Matter and Complex Systems,2002,26:521-529.
[22]Boguna M, Pastor-Satorras R, Vespignani A. Epidemic spreading.in complex networks with degree correlations[J]. Physics and Astronomy,2003, 625:127-147.
[23]Boguna M, Pastor-Satorras R. Epidemic spreading in correlated complex networks[J]. Physical Review E,2002,66:047104(1-4).
[24]Bailey N T J. The Mathematical Theory of Infectious Diseases and Its Applications[M]. New York:Hafner Press,1975.
[25]Anderson R M, May R M. Infectious Diseases in Humans[M]. Oxford:Oxford University Press,1992.
[26]Lloyd-Smith J 0, Schreiber S J, Lopp P E, Getz W M. Superspreading and the effect of individual variation on disease emergence[J]. Nature,2005, 438(7066):355-359.
[27]Galvani A P, May R M. Epidemiology:Dimensions of superspreading[J]. Nature, 2005,438(7066):293-295.
[28]Chu X W, Zhang Z Z, Guan J H, Zhou S G. Epidemic spreading with nonlinear infectivity in weighted scale-free networks[DB/OL].2009, arxiv:0903.0924vl.
[29]Colizza V, Pastor-Satorras R, Vespignani A. Reaction-diffusion processes and metapopulation models in heterogeneous networks[J]. Nature Physics,2007, 3:276-282.
[30]Baronchelli A, Catanzaro M, Pastor-Satorras R. Bosonic reaction-diffusion processes on scale-free networks[J]. Physical Review E,2008,78:016111.
[31]Zhou J, Liu Z H. Epidemic spreading in communities with mobile agents[J]. Physica A,2009,388:1228-1236.
[32]Zhou J, Liu Z H. Epidemic spreading in complex networks [J]. Frontiers of Physics in China,2008,3(3):331-348.
[33]Wu X Y, Liu Z H. How community structure influences epidemic spread in social networks[J]. Physica A,2008,387:623-630.
[34]Tang M, Liu L, Liu Z H. Influence of dynamical condensation on epidemic spreading in scale-free networks[J]. Physical Review E,2009,79:016108.
[35]Zhou Y Z, Liu Z H, Zhou J. Periodic wave of epidemic Spreading in community Networks[J]. Chinese Physics Letters,2007,24(2):581-584.
[36]Ball F, sirl D, Trapman P. Threshold behavior and final outcome of an epidemic on a random network with household structure[J]. Advances in Applied Probability 2009,41(3):765-796.
[37]Nekovee M, Moreno Y, Bianconi G, Marsili M. Theory of rumor spreading in complex social networks[J]. Physica A:Statistical Mechanics and its Applications, 2007,374(1):457-470.
[38]Barthelemy M, Barrat A, Pastor-Satorras R, Vespignani A. Velocity and hierarchical spread of epidemic outbreaks in scale-free networks[J]. Physical Review Letters,2004,92(17):178701.
[39]Xia C Y, Liu Z X, Chen Z Q, et al. Dynamic spreading behavior of homogeneous and heterogeneous networks[J]. Progress in Natural Science,2007, 17(3):358-365.
[40]Xia C Y, Liu Z X, Chen Z Q, et al. Epidemic spreading behavior on local-world evolving networks[J]. Progress in Natural Science,2008,18(6):653-658.
[41]Xia C Y, Liu Z X, Chen Z Q, et al. A new multistage epidemiological model on complex networks[J]. Dynamics of Continuous, Discrete, and Impulsive Systems-Series B,2007,14(S6):160-165.
[42]Zheng D F, Hu P M, Trimper S. Epidemics and dimensionality in hierarchical networks[J]. Physica A,2005,352:659-668.
[43]Li X, Wang X F. Controlling the spreading in small-world evolving networks: stability, oscillation, and topology[C]. IEEE Transactions on Automatic Control,2006,51 (3):534-540.
[44]Gross T, D'Lima C J D, Blasius B. Epidemic dynamics in an adaptive networks [J]. Physical Review Letters,2006,96:208701.
[45]Xu X J, Zhang X, Mendes J F F. Impacts of preference and geography on epidemic spreading[J]. Physical Review E,2007,76:056109.
[46]Karrer B, Newman M E J. A message passing approach for general epidemic models[DB/OL].2010, arXiv:1003.5673v1.
[47]Eguiluz V M, Klemm K. Epidemic threshold in structured scale-free networks[J]. Physical Review Letters, 2002,89(10):108701.
[48]Y. Moreno, J. B. Gomez, Pacheco A F. Epidemic incidence in correlated complex networks[J]. Physical Review E,2003,68(3):035103.
[49]Joo J, Lebowitz J L. Behavior of susceptible-infected-susceptible epidemics on heterogeneous networks with saturation[J]. Physical Review E,2004, 69(6):066105.
[50]Grabowski A, Kosinski R A. Epidemic spreading in a hierarchical social network[J]. Physical Review E,2004,70(3):031908.
[51]Xu X J, Wang W X, Zhou T, Chen G. Geographical effects on epidemic spreading in scale-free networks[J]. Computational Physics and Physical Computation, 2006,17(12):1815-1822.
[52]许丹,李翔,汪小帆.局域世界复杂网络中的病毒传播及其免疫控制[J].控制与决策,2006,21(7)：817-820.
[53]许田,张培培,姜玉梅,苏蓓蓓,何大韧.流行病传播模型与SARS[J].自然杂志,2003,26(1)：20-25.
[54]杨洪勇,张嗣赢.基于复杂网络的禽流感病毒传播[J].系统仿真学报,2008,20(18)：5001-5005.
[55]Bai W J, Zhou T, Wang B H. Interplay between HIV/AIDS epidemics and demographic structures based on sexual contact networks[DB/OL].2006, arxiv:0602137.
[56]Han X P, Wang B H, Zhou C S, Zhou T, Zhu J F. Scaling in the Global Spreading Patterns of Pandemic Influenza A and the Role of Control:Empirical Statistics and Modeling[DB/OL].2009, arXiv:0912.1390.
[57]Barabasi A L, Albert R, Jeong H. Mean-field theory for scale-free random networks[J]. Physica A,1999,272:173-187.
[58]吴建军.城市交通网络拓扑结构复杂性研究[D].北京交通大学,2008,P20-21.
[59]Watts D J. Small Worlds:The dynamics of networks between order and randomness[M]. Princeton University Press,1999.
[60]Newman M E J, Girvan M. Finding and evaluating community structure in networks[J]. Physical Review E,2004,69:026113.
[61]Newman M E J. Scientific collaboration networks:Ⅱ. Shortest paths, weighted networks, and centrality[J]. Physical Review E,2001,64:016132.
[62]Newman M E J. The structure and function of complex networks[J]. SIAM Review,2003, 45:167-256.
[63]Newman M E J. Scientific collaboration networks. I. Network construction and fundamental results[J]. Physical Review E,2001,64:016131.
[64]Barrat A, Weigt M. On the properties of small world networks [J]. The European Physical Journal B,2000,13:547-560.
[65]Alon N, Yuster R, Zwick U. Finding and counting given length cycles[J]. Algorithmica,1997,17:209-223.
[66]李晓佳,张鹏,狄增如,樊瑛.复杂网络中的社团结构[J].复杂系统与复杂性科学,2008,5(3)：19-42.
[67]Newman M E J, Watts D J. Renormalization group analysis of the small-world network model[J]. Physical Letters A,1999,263:341-346.
[68]Newman M E J. The structure and function of networks[J]. Computer Physics Communication,2002,147:40-45.
[69]Liu Z H, et al. Connective distribution and attack tolerance of general networks with both preferential and random attachments[J]. Physics Letters A,2002, 303:337-344.
[70]Shi D H, Chen Q H, Liu L M. Markov chain-based numerical method for degree distribution of growing networks[J]. Physical Review E,2005,71:036140.
[71]Bollobas B, Riordan 0. Mathematical results on scale-free random graphs[M]. In:Bornholdt, S, Schuster H G(ed.) Handbook of Graphs and Networks:From the Genome to the Internet, Berlin:Wiley-VCH,2003,1-34.
[72]Cohen R, Havlin S. Scale-free networks are ultra small[J]. Physical Review Letters,2003,90:058701.
[73]Krapivsky P L, Redner S, Leyvraz F. Connectivity of growing random networks[J]. Physical Review Letters,2000,85:4629-4632.
[74]Dorogovtsev S N, Mendes J F F, Samukhin A N. Structure of growth networks with preferential linking[J]. Physical Review Letters.2000,85:4633-4636.
[75]Fronczak A, Fronczak P, and Holyst J A. Mean-field theory for clustering coefficients in Barabasi-Albert networks[J]. Physical Review E 64,2001, 026118.
[76]邵峰晶,于忠清,王金龙,孙仁诚.数据挖掘原理与算法(第二版)[M].北京：科学出版社,2009.8.
[77]Agrawal R, Imielinski T, Swami A. Mining Associations between Sets of Items in Massive Databases[C]. Process of the ACM-SIGMOD 1993 Int'1 Conference on Management of Data, Washington D.C., May 1993.
[78]Han J W, Pei J. FreeSpan:Frequent pattern projected sequential pattern mining[C]. International Conference on Knowledge Discovery and Data Mining, Proceedings of the sixth ACM SIGKDD international conference on Knowledge discovery and data mining, Boston:MAACM Press,2000,355-359.
[79]Han J W, Pei J. PrefixSpan:Mining sequential patterns efficiently by prefix-projected pattern growth[C]. IEEE Transactions on Knowledge and Data Engineering,2004,1-17.
[80]Han J W, Pei J, Yin Y W. Mining frequent patterns without candidate generation[C]. Proceedings of ACM SIGMOD Intl. Conference on Management of Data, Dallas:ACM Press,2000,1-12.
[81]Agrawal R, Srikant R. Mining sequential patterns:Generalization and performance improvement[C]. In:Proc of the 5th International Conference on Extending Database Technology (EDB T96). Berlin:Springer Verlag,1996,3-17.
[82]mannila H, Toivonen H, Verkamo A I. Discovery of frequent episodes in event sequences[J]. Data Mining and Knowledge Discovery,1997,1:259-289.
[83]Agrawal R, Srikant R. Mining quantitative association rules in large relational tables[C]. In proc.1996 ACM-SIGMOD Int. Conf. Management of Data, pages, Montreal, Canada,1996.6,1-12.
[84]Zaki M J. SPADE:An efficient algorithm for mining frequent sequences[J]. Machine Learning,2001,42(1-2):31-60.
[85]Shao F J, Sun R C, Yu Z Q. An Outlier-analysis algorithm based on the reduction of boundary cells influence[C]. Proc. Of the 8th Joint International Computer Conference,2002,536-540.
[86]高俊,施伯乐.快速关联规则挖掘算法研究[J].计算机科学,2005,32(3)：200-201.
[87]Li Y C, Chang C C. A new FP-tree algorithm for mining frequent itemsets[C]. AWCC 2004. LNCS 3309,2004,26-277.
[88]Han J, Pei J, Yin Y, Mao R. Mining frequent patterns without candidate generation:A Frequent pattern tree approach[J]. Data Mining and knowledge Discovery,2004.8,53-87.444.
[89]Bennett K P. Combining support vector and mathematical programming methods for classification. Advances in kernel methods:support vector learning[M], MIT Press,1999, P307-326.
[90]Vapnik V. Statistical learning theory[M]. New York:Wiley,1998.
[91]Gunn S R. Support vector machines for classification and regression[C]. ISIS Technical Report,1998.
[92]Gibson D, Kleinberg J M K, Raghavan P. Inferring web communities from link topology[C]. In Proceedings of the 9th ACM Conference on Hypertext and Hypermedia, Association of Computing Machinery, New York,1998.
[93]Flake G W, Lawrence S, Giles C L, Coetzee F M. Self-Organization and identification of Web communities[J]. IEEE Computer,2002,35(3):66-71.
[94]Guimera R, Amaral L A N. Functional cartography of complex metabolic networks[J]. Nature,2005,433(7028):895-900.
[95]Wu J J, Gao Z Y, Sun H J. Cascade and breakdown in scale-free networks with community structure[J]. Physical review E, Statistical, nonlinear, and soft matter physics,2006,74(6 Pt 2):066111.
[96]Leon D, Alex A, Albert D G. Impact of community structure on information transfer[J]. Physical review. E, Statistical, nonlinear, and soft matter physics,2008,77(3 Pt 2):036103.
[97]Girvan M, Newman M E J. Community structure in social and biological networks[C]. Proc. of the National Academy of Science,2002,9(12):7821-7826.
[98]Tyler J R, Wilkinson D M, Huberman B A. Email as spectroscopy:Automated discovery of community structure within organizations[C]. In:Huysman M, Wenger E, Wulf V, eds. Proc. of the 1st Int'1 Conf. on Communities and Technologies. Dordrecht:Kluwer Academic Publishers,2003,81-96.
[99]Palla G, Derenyi I, Farkas I, Vicsek T. Uncovering the overlapping community structure of complex networks in nature and society[J]. Nature,2005, 435(7043):814-818.
[100]Ravasz E, Somera A L, Mongru D A. Hierarchical organization of modularity in metabolic networks[J]. Science,2002,297(5586):1551-1555.
[101]Wang Z, Zhang J. In search of the biological significance of modular structures in protein networks[J]. PLOS Computational Biology,2007,3(6):107.
[102]Spirin V, Mirny L A. Protein complexes and functional modules in molecular networks[C]. Proc. of the National Academy of Science,2003, 100(21):12123-12128.
[103]Li X, Liu B, Yu PS. Discovering overlapping communities of named entities[C]. In:Furnkranz J, Scheffer T, Spiliopoulou M, eds. Proc. of the 10th European Conf. on Principles and Practice of Knowledge Discovery in Databases. Berlin: Springer-Verlag,2006,593-600.
[104]Ino H, Kudo M, Nakamura A. Partitioning of Web graphs by community topology[C]. In:Ellis A, Hagino T, eds. Proc. of the 14th Int'1 Conf. on World Wide Web. New York:ACM Press,2005,661-669.
[105]Sidiropoulos A, Pallis G, Katsaros D, Stamos K, Vakali A, Manolopoulos Y. Prefetching in content distribution networks via Web communities identification and outsourcing[J]. World Wide Web,2008,11(1):39-70.
[106]Almeida R B, Almeida V A F. A community-aware search engine[C]. In:Feldman SI, Uretsky M, Najork M, Wills CE, eds. Proc. of the 13th Int'1 Conf. on World Wide Web. New York:ACM Press,2004,413-421.
[107]Ghosh R, Lerman K. Community detection using a measure of global influence[C]. In Proceedings of KDD workshop on Social Network Analysis (SNAKDD),2008, eprint arXiv:0805.4606.
[108]Arenas A, Duch J, Fernandez A, Gomez S. Size reduction of complex networks preserving modularity[J]. New Journal of Physics,2007,9:176.
[109]Leicht E A, Newman M E J. Community structure in directed networks [J]. Physical Review Letters,2008,100(11):118703.
[110]Santo F. Community detection in graphs[J]. Physics Reports,2010, 486(3-5):75-174.
[111]Burt R S. Positions in networks[J]. Soc. Forces,1976,55:93.
[112]Wasserman S, Faust K. Social network analysis[M]. Cambridge University Press, Cambridge, UK.1994.
[113]Fouss F, Renders J M. Random-walk computation of similarities between nodes of a graph with application to collaborative recommendation[J]. IEEE Trans. on Knowledge and Data Eng. member-Pirotte, Alain and Member-Saerens, Marco. 2007,19(3):355.
[114]Saerens M, Fouss F, Yen L, Dupont P. The Principal Components Analysis of a Graph and its Relationships to Spectral Clustering[C]. Proceedings of the 15th European Conference on Machine Learning (ECML 2004). Lecture Notes in Artificial Intelligence, Pisa, Italy,2004, p371-383.
[115]Yen L, Fouss F, Decaestecker C, Francq P, Saerens M. Graph Nodes Clustering Based on the Commute-Time Kernel[C]. In PAKDD,2007, P1037-1045.
[116]Yen L, Fouss F, Decaestecker C, Francq P, Saerens M. Graph nodes clustering with the sigmoid commute-time kernel:A comparative study [J]. Data & Knowledge Engineering,2009,68(3):338-361.
[117]Zhou H. Distance, dissimilarity index, and network community structure[J]. Physal Review E,2003,67(6):061901.
[118]Palmer C R, Faloutsos C. Electricity Based External Similarity of Categorical Attributes[C]. In Proceedings of PAKDD,2003, P486-500.
[119]Tong H, Faloutsos C, Pan J Y. Random walk with restart:fast solutions and applications[J]. Knowledge and Information Systems,2008,14(3):327-346.
[120]Gori M, Pucci A. ItemRank:A random-walk based scoring algorithm for recommender engines[C]. In IJCAI'07:Proceedings of the 20th international joint conference on Artificial intelligence,2007,2766-2771.
[121]Brin S, Page L. The anatomy of a large-scale hypertextual Web search engine [J]. Computer Networks and ISDN Systems,1998,30(1-7):107.
[122]Estrada E, Hatano N. Communicability in complex networks[J]. Physical Review E,2008,77(3):036111.
[123]Estrada E, Hatano N. Communicability graph and community structures in complex networks[J]. Applied Mathematics and Computation,2009,214(2):500-511.
[124]Zhu X J. Semi-Supervised Learning with Graphs [D]. Carnegie Mellon University, CMU-LTI-05-192,2005.
[125]Donath W, Hoffman A. Lower bounds for the partitioning of graphs [J]. IBM Journal of Research and Development,1973,17(5):420.
[126]Fiedler M. Algebraic connectivity of graphs[J]. Czechoslovak Mathematical Journal,1973,23 (98):298-305.
[127]Spielman D A, Teng S H. Spectral Partitioning Works:Planar Graphs and Finite Element Meshes[C]. IEEE Symposium on Foundation of Computer Science,1996, 96-105.
[128]Fortunato S. Community detection in graphs[DB/OL]. arXiv:0906.0612v2,2009.6.
[129]Kernighan B W, Lin S. An efficient heuristic procedure for partitioning graphs[J]. Bell System Technical Journal,1970,49:291-307.
[130]Newman M E J, Girvan M. Detecting community structure in networks[J], The European Physical Journal B,2004,38:321-330.
[131]Radicchi F, Castellano C, Cecconi F, et al. Defining and identifying communities in networks [J]. Proceedings of the National Academy Sciences of the USA,2004, 101(9):2658-2663.
[132]Latora V, Marchion M. Efficient behavior of small-world networks [J]. Physical Review Letters,2001,87(19):198701.
[133]Latora V, Marchiori M. Economic small-world behavior in weighted networks[J]. The European Physical Journal B,2003,32:249-263.
[134]Latora V, Marchiori M. A measure of centrality based on the network efficiency[J]. New Journal of Physics,2007,9:188.
[135]Fortunato S, Latora V, Marchiori M. Method to find community structures based on information centrality[J]. Physical review E,2004,70(5):056104.
[136]Hastie T, Tibshirani R, Friedman J H. The Elements of Statistical Learning[M]. Springer, Berlin, Germany, ISBN 0387952845 2001.
[137]汪小帆,刘亚冰.复杂网络中的社团结构算法综述[J].电子科技大学学报,2009(9),38(5)：537-543.
[138]Zachary W W. An information flow mode1 for conflict and fission in small groups[J]. Journal of Anthropological Research,1977,33(4):452-473.
[139]Pang C J, Shao F J, Sun R C. Detecting Community Structure in Networks by Propagating Labels of Nodes[C]. Sixth International Symposium on Neural Networks, ISNN2009, WuHan, China. (ISSN2009).2009.5.839-846.
[140]Mendes J F F, Dorogovtsev S N, and Ioffe A F. Evolution of networks:From Biological Nets to the Internet and WWW[M]. Oxford:Oxford University Press, 2003.
[141]Latora V, Marchiori M. Is the Boston subway a smallworld network? [J] Physica A,2002,314:109-113.
[142]Sen P, Dasgupta S, Chatterjee A. Small-world properties of the Indian railway network[J]. Physical Review E,2003,67:036106.
[143]Seaton K A, Hackett L M. Stations, trains and small-world networks [J]. Physica A,2004,339:635-644.
[144]Jiang B, Claramunt C. Topological analysis of urban street networks[J]. Environment and Planning B,2004,31:151-162.
[145]Li W, Cai X. Statistical analysis of airport network of China[J]. Physical Review E,2003,69:046106.
[146]Guimera R, Mossa S, Turtschi A, Amaral L A N. The worldwide air transportation network:Anomalous centrality,community structure, and cities' global roles[J]. PNAS,2005,102:7794-7799.
[147]Wu J J, Gao Z Y, Sun Huijun. Urban transit system as a scale-free network[J]. Modern Physics Letters B,2004,18:1043-1049.
[148]Lu H P, Shi Y. Complexity of Public Transport Networks[J]. TSINGHUA SCIENCE AND TECHNOLOGY.2007,12(2):204-213.
[149]Xu X P, Hu J H, Liu F, Liu L S. Scaling and correlations in three bus-transport networks of China[J]. Physical A,2007,374:441.
[150]常鸣,马寿峰.我国大城市公交网络结构的实证研究[J].系统工程学报.2007,22(04)：412-418.
[151]Sun R C, Shao F J. Analysis of Qingdao's Public Transport Line Network[C]. 2008 IEEE International Conference on Automation and Logistics (ICAL 2008), 2008.9,1147-1150.
[152]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.
[153]王喆, 彭其渊.成都市公交复杂网络拓扑特性研究[J].交通与计算机,2007,25(2)：39-42.
[154]李英,周伟,郭世进.上海公共交通网络复杂性分析[J].系统工程,2007,25(1)：38-41.
[155]张晨,张宁.上海市公交网络拓扑性质研究[J].上海理工大学学报,2006,28(5)：489-494.
[156]冷静.青岛城市空间结构的变迁与发展[N].青岛日报,2009.9.1.
[157]Hethcote H W. The mathematics of infectious diseases[J]. SIAM Review,2000, 42(4):599-653.
[158]郭雷,许晓鸣 主编.复杂网络[M].上海：上海科技教育出版社,2006：115-140.
[159]Das Bistro Project's anti-code-red default.ida. http://www.dasbitro.com/default.ida.
[160]Liljenstam M, Nicol D. Comparing passive and active worm defenses[C]. Proceedings of the 1st International Conference on Quantitative Evaluation of Systems (QEST),2004 September.
[161]Nicol D, Liljenstam M. Models of active worm defenses[C]. Proceedings of the IPSI Studenica Conference,2004 June.
[162]杨峰,段海新,李星.网络蠕虫扩散中蠕虫和良性蠕虫交互过程建模与分析[J].中国科学E辑信息科学,2004,34(8)：841-856.
[163]Newman M E J. Threshold effects for two pathogens spreading on a network[J]. Physical Review Letters,2005,95:108701.
[164]Ahn Y Y, Masuda N, Jeong H, Noh J D. Epidemic dynamics of Interacting two particle species on scale-free networks[J]. Physical Review E,2006, 74(6):066113.
[165]Moore C, Newman M E J. Epidemics and percolation in small-world networks [J]. Physical Review E,2000,61:5678-5682.
[166]Moore C, Newman M E J. Exact solution of site and bond percolation on small-world networks[J]. Physical Review E,2000,62:7059-7064.
[167]Newman M E J, Jensen I, Ziff R M. Percolation and epidemics in a two-dimensional small world[J]. Physical Review E,2002,65:021904.
[168]Abramson G. Kuperman M, Social games in a social network[J]. Physical Review E,2001,63(3):030901.
[169]Agiza H N, Elgazzar A S, Youssef S A. Phase transitions in some epidemic models defined on small-world networks[DB/OL].2003, arXiv:0301004.
[170]周涛,傅忠谦,牛永伟,王达,曾燕,汀秉宏,周佩玲.复杂网络上传播动力学研究综述[J].自然科学进展,2005,15(5)：513-518.
[171]Pastor-Satorras R. and Vespignani A. Epidemics and immunization in scale-free networks[M]. In:Bornholdt S, Schuster HG(eds.) Handbook of Graph and Networks. Berlin:Wiley-VCH,2003.
[172]Barabasi A L, Albert R, and Jeong H. Scale-free characteristics of random networks:the topology of the world-wide web[J]. Physica A,2000,281:69-77.
[173]Price D J. Networks of scientific papers [J]. Science,1965,149:510-515.
[174]Gross T, Blasius B. Adaptive coevolutionary networks:a review[J]. Journal of the royal society interface,2008,5:259-271.
[175]Gross T, Kevrekidis I G. Coarse-graining adaptive coevolutionary network dynamics via automated moment closure[DB/OL].2007, arXiv:0702047.
[176]Ehrhardt, George C M A, Marsili M. Vega-Redondo F. Phenomenological models of socio-economic network dynamics[J]. Physical Review E,2006,74:036106-11.
[177]Zanette D. Coevolution of agents and networks in an epidemiological model [DB/OL].2007, arXiv:0707.
[178]Zanette D H, Gil S. Opinion spreading and agent segregation on evolving networks [J]. Physica D,2006,224:156-165.
[179]Gil S, Zanette D H. Coevolution of agents and networks:opinion spreading and community disconnection[J]. Physical Letters A,2006,356:89-95.
[180]Holme P, Newman M E J. Nonequilibrium phase transition in the coevolution of networks and opinions[J]. Physical Review E,2007,74:056108-5.
[181]Keeling M J, Rand D A, Morris A J. Correlation models for childhood epidemics[J]. Proceedings the Royal Society B,1995,264:1149-1156.
[182]Holme P, Kim B J. Growing scale-free networks with tunable clustering[J]. Physical Review E,2002,65:026107.
[183]Tian L, Zhu C P, Shi D N, Gu Z M. Universal scaling behavior of clustering coefficient induced by deactivation mechanism[J]. Physical Review E,2006, 74:046103.
[184]Volz E, Meyers L A. Susceptible-infected-recovered epidemics in dynamic contact networks[C]. Proceedings of the Royal Society B:Biological Sciences, 2007,274(1628):2925-2933.
[185]Fefferman N H, Ng K L. How disease models in static networks can fail to approximate disease in dynamic networks[J]. Physical Review E,2007, 76:031919.
[186]Shaw L B, Schwartz I B. Rewiring for adaptation[J]. Physics,2010,3.17.
[187]Shaw L B, Schwartz I B. In Adaptive Networks:Theory, Models and Applications, edited by T[DB/OL]. Gross and H. Sayama (Springer/NECSI,2009), Studies on Complexity Series.
[188]Boguna M, Pastor-satorras R, Vespignani A. Stochastic theory of synchronization transitions in extended systems[J]. Physical Review Letters, 2003,90(20):204101.
[189]Sienkiewicz J, Holyst J A. Statistical analysis of 22 public transport networks in Poland[J].2005, arxiv:0506074.
[190]Ferber C V, Holovatch Y, Palchykov V. Scaling in publictransport networks [J]. 2005, arxiv:0501296.
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