Jeong 2000 Nature Archae Becterium Eukaryote 43 Metabolic

Jeong, 2000, Nature 包括太古代（ Archae），细菌（ Becterium), 真核生物（Eukaryote）在内的 43个物种的 新陈代谢网（ Metabolic network ）都是 Scale-free的。 4

Protein-protein interaction networks Rui-Sheng Wang, Yong Wang, Ling-Yun Wu, Xiang-Sun Zhang, Luonan Chen. Analysis on multi-domain cooperation for predicting protein-protein interactions. BMC Bioinformatics, 8: 391, 2007 Shihua Zhang, Xue-Mei Ning and Xiang-Sun Zhang. Identification of functional modules in a PPI network by clique percolation clustering. Computational biology and chemistry, 30(6), 445 -451, 2006. Luonan Chen, Ling-Yun Wu, Yong Wang and Xiang-Sun Zhang. Inferring Protein Interactions from Experimental Data by Association Probabilistic Method. Proteins: Structure, Function, and Bioinformatics, Vol. 62, pp. 833 -837, 2006. Xiang-Sun Zhang, Rui-Sheng Wang, Ling-Yun Wu, Shihua Zhang and Luonan Chen. Inferring Protein-Protein Interactions by Combinatorial Models. IFMBE Proceedings, Vol. 14, 2006, 183 --186, Springer Berlin Heidelberg. 5

Metabolic and signaling networks Zhenping Li, Rui-Sheng Wang, Xiang-Sun Zhang and Luonan Chen. Detecting drug targets with minimum side effects in metabolic networks. IET Systems Biology, 3(6), 523 -533, 2009 Zhenping Li, Rui-Sheng Wang, Xiang-Sun Zhang. Mass Flow Model and Essentiality of Enzymes in Metabolic Networks. Lecture Notes in Operations Research, 9, pp. 182 -190, World Publishing Corporation, Lijiang, 2008. Jin G, Zhou X, Wang H, Zhao H, Cui K, Zhang XS, Chen L, Hazen SL, Li K, Wong ST The Knowledge-Integrated Network Biomarkers Discovery for Major Adverse Cardiac Events. J Proteome Res 7(9): 4013 -4021, 2008 6

Book about Biomolecular networks 7 Luonan Chen, Rui-Sheng Wang, Xiang-Sun Zhang. Biomolecular Networks: Methods and Applications in Systems Biology. John Wiley & Sons, Hoboken, New Jersey. July, 2009.

Yeast functional linkage network SCIENCE Vol 306(26) 2004 DNA damage module 可分成 564 个模块，由 950 个显著的块间相互 作用相连接。

Importance of the topic Girvan, M, Newman, M. , Proc. Natl. Acad. Sci, 2002 Ravasz, E, Somera, A, Mongru, D, Oltvai, Z, Barabasi, A. , Science, 2002 Radicchi, F, Castellano, C, Cecconi, F. , Proc. Natl. Acad. Sci, 2004 Guimera, R, Mossa, S, Turtschi, A. , Proc. Natl. Acad. Sci, 2005 Guimera, R, Amaral, L. , Nature, 2005 Newman, M. , Proc. Natl. Acad. Sci, 2006 Rosvall, M, Bergstrom, C. , Proc. Natl. Acad. Sci, 2007 Fortunato, S, Barthelemy, M. , Proc. Natl. Acad. Sci, 2007 生物信息学与最优化方法 14 Weinan, E, Li, T, Vanden-Eijnden, E. , Proc. Natl. Acad. Sci,

社团结构探索方法概述 A large number of methods have been developed for detecting communities, which can be generally categorized into local and global methods. Local methods （局部方法） for community detection identify a subset of nodes as a community according to certain local connection conditions, independently from the structure of the rest of the network. Such methods include clique overlap-based hierarchical clustering, clique percolation method, and sub-graph fitness method. Global methods （全局方法）for community detection optimize certain global quantitative functions encoding the quality of the overall partition of the network, such as information theoretical method, Potts model, and optimization of modularity measures. 15

l我们小组在研究这一问题的早期发展了一些基于图论和 矩阵谱分解的模块探测算法 (local method) Shihua Zhang, Rui-Sheng Wang, and Xiang-Sun Zhang. Identification of overlapping community structure in complex networks using fuzzy cmeans Clustering. Physica A, 2007, 374, 483– 490. Shihua Zhang, Rui-Sheng Wang and Xiang-Sun Zhang. Uncovering fuzzy community structure in complex networks. Physical Review E, 76, 046103, 2007 Rui-Sheng Wang, Shihua Zhang, Yong Wang, Xiang-Sun Zhang, Luonan Chen. Clustering complex networks and biological networks by nonnegative matrix factorization with various similarity measures. Neurocomputing, 2007 16

极端例子：ring of cliques Fortunato & Barthelemy, Proc. Natl. Acad. Sci. USA 104 (1), 36 -41 (2007) 19

提出新的模块化指标D值 模块化密度函数 D: Zhenping Li, Shihua Zhang, Rui-Sheng Wang, Xiang-Sun Zhang, Luonan Chen, Quantitative function for community detection. Physical Review E, 77, 036109, 2008 20

D值克服了Q值存在的 resolution limit 问题 21

错分现象---Misidentification 用Q或D作优化可能得到不满足定义的模块 Q partitions the network into three communities (two Kn and one K 5) when n>=16 (respectively, n>=21), in which K 5 is a sub-graph violating all reasonable community definition. Xiang-Sun Zhang, Rui-Sheng Wang, Yong Wang, Ji-Guang Wang, Yu-Qing Qiu, Lin Wang, and Luonan Chen. Modularity optimization in community detection of complex networks. Europhysics Letters (EPL), 87, 2009. 被评为 EPL 2009 best paper 23

Finding 1 对

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为了彻底解决这些问题 提出一个新的 OR 模型和相应的算法，这一算法不会产生 resolution limit 和 mis-identification 现象 关键思路：模块分划质量函数的定义要包含社团定义。 Xiang-Sun Zhang, Zhenping Li, Rui-Sheng Wang, Yong Wang. A combinatorial model and algorithm for globally searching community structure in complex networks Journal of Combinatorial Optimization (JCO), 2010. DOI: 10. 1007/s 10878 -010 -9356 -0 33

A new OR model Problem definition: Given a network, the community identification problem is to partition the network into as many non-overlapping sub-networks as possible such that each sub-network satisfies a given community definition. 给定一个网络和一个社团的定义，社团结构识别 的问题就是将整个网络分成尽可能多的满足社团定 义的子网络。 34

A qualified min-cut (QMC) algorithm A heuristic principle is given to find a feasible partition with the largest number of communities. It is realized by a min-cut operation: A min- cut operation is called qualified if the two resulting sub-networks satisfy the module definition. The community identification problem can be 36 solved based on a series of qualified min-cut operations.

Experiment results (artificial networks) Rings of cliques 37 Uneven ad-hoc network

Experiment results (real networks) Football team network 38 Jazz musician network

学术性的，实用性的问题远远没有解决 Yong-Yeol Ahn, James P. Bagrow & Sune Lehmann， Nature, 2010 Link communities reveal multiscale complexity in networks 39

致谢 This work is cooperated with Dr. 李珍萍，Dr. 王瑞省，Dr. 王勇，Dr. 张世华， Dr. 王吉光，Dr. 张俊华 This work is supported by 国家自然科学重点基金 10631070 973项目 2066 CB 503905 国家自然科学基金项目 60873205 40

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