在論文中，我們對於社群定義和社群強度評估發展了一套完整架構，不僅提供深入的物理現象觀察，對各種網路分析方法也能有統一的解釋。並針對區域社群偵測問題提出一個能保證偵測結果之社群強度的演算法。
在我們的架構之中，其中一個關鍵的創新就是在網路結構分析中提出了一個新穎的概念「相對重要性」。基於相對重要性，我們定義了社群強度的量測方式。而社群則定義為一組社群強度不為負值的節點集合。基於社群的定義，我們也證明一些對於社群的數學等價描述，並能解釋它們的社會意義。我們也展示社群強度和導度(conductance)的相關性，並定義一個網路的模塊性(modularity)為其子圖社群強度的加權平均。在這樣的定義下，不僅概括了原來模塊性的定義，也能解釋穩定性(stability)為我們的一種特殊情形。
而針對區域社群問題，我們發展了一套凝聚型的演算法，可以保證偵測結果之社群強度。該演算法有兩個良好性質：只需探索相鄰集合(neighboring set)中的節點資訊，並能藉由遞迴公式快速更新相對重要性。因此，我們的演算法的不僅複雜度與參考文獻[4]中的演算法相近，更能考慮群聚係數(clustering coefficient)的影響。最後，從我們的實驗結果可以看出，對於社群強度較強的節點集合，我們的演算法的偵測結果可以達到100%的查準率(precision)和查全率(recall)。

[1] Mark EJ Newman and Michelle Girvan. Finding and evaluating community structure in networks. Physical review E, 69(2):026113, 2004.
[2] Renaud Lambiotte. Multi-scale modularity in complex networks. In Modeling and
Optimization in Mobile, Ad Hoc and Wireless Networks (WiOpt), 2010 Proceedings
of the 8th International Symposium on, pages 546-553. IEEE, 2010.
[3] J-C Delvenne, Sophia N Yaliraki, and Mauricio Barahona. Stability of graph communities across time scales. Proceedings of the National Academy of Sciences,
107(29):12755-12760, 2010.
[4] Aaron Clauset. Finding local community structure in networks. Physical review E,
72(2):026132, 2005.
[5] Michelle Girvan and Mark EJ Newman. Community structure in social and biological networks. Proceedings of the National Academy of Sciences, 99(12):7821-7826, 2002.
[6] Tiantian Zhang and Bin Wu. A method for local community detection by finding
core nodes. In Advances in Social Networks Analysis and Mining (ASONAM), 2012
IEEE/ACM International Conference on, pages 1171-1176. IEEE, 2012.
[7] Ulrik Brandes, Garry Robins, Ann Mccranie, and Stanley Wasserman. What is
network science? Network Science, 1(1).
[8] Filippo Radicchi, Claudio Castellano, Federico Cecconi, Vittorio Loreto, and
Domenico Parisi. Defining and identifying communities in networks. Proceedings
of the National Academy of Sciences of the United States of America, 101(9):2658-
2663, 2004.
[9] Yanqing Hu, Hongbin Chen, Peng Zhang, Menghui Li, Zengru Di, and Ying
Fan. Comparative definition of community and corresponding identifying algorithm.
Physical Review E, 78(2):026121, 2008.
[10] Reid Andersen, Fan Chung, and Kevin Lang. Local graph partitioning using pagerank vectors. In Foundations of Computer Science, 2006. FOCS'06. 47th Annual
IEEE Symposium on, pages 475-486. IEEE, 2006.
[11] Reid Andersen and Kevin J Lang. Communities from seed sets. In Proceedings of the 15th international conference on World Wide Web, pages 223-232. ACM, 2006.
[12] Jure Leskovec, Kevin J Lang, Anirban Dasgupta, and Michael W Mahoney. Statistical properties of community structure in large social and information networks. In Proceedings of the 17th international conference on World Wide Web, pages 695-704.ACM, 2008.
[13] Santo Fortunato. Community detection in graphs. Physics Reports, 486(3):75-174,2010.
[14] Duncan JWatts and Steven H Strogatz. Collective dynamics of small-worldnetworks. nature, 393(6684):440-442, 1998.
[15] Gergely Palla, Imre Derenyi, Illes Farkas, and Tamas Vicsek. Uncovering the overlapping community structure of complex networks in nature and society. Nature,
435(7043):814-818, 2005.
[16] Mark EJ Newman. Fast algorithm for detecting community structure in networks.
Physical review E, 69(6):066133, 2004.
[17] Peter J Mucha, Thomas Richardson, Kevin Macon, Mason A Porter, and Jukka-
Pekka Onnela. Community structure in time-dependent, multiscale, and multiplex
networks. Science, 328(5980):876-878, 2010.
[18] Brian Karrer, Elizaveta Levina, and Mark EJ Newman. Robustness of community structure in networks. Physical Review E, 77(4):046119, 2008.
[19] Jure Leskovec, Kevin J Lang, and Michael Mahoney. Empirical comparison of algorithms for network community detection. In Proceedings of the 19th international
conference on World wide web, pages 631-640. ACM, 2010.
[20] Jaewon Yang and Jure Leskovec. Defining and evaluating network communities
based on ground-truth. In Proceedings of the ACM SIGKDD Workshop on Mining
Data Semantics, page 3. ACM, 2012.
[21] Martin Rosvall and Carl T Bergstrom. An information-theoretic framework for
resolving community structure in complex networks. Proceedings of the National
Academy of Sciences, 104(18):7327-7331, 2007.
[22] Martin Rosvall and Carl T Bergstrom. Maps of random walks on complex networks reveal community structure. Proceedings of the National Academy of Sciences,105(4):1118-1123, 2008.
[23] Stephen Boyd, Arpita Ghosh, Balaji Prabhakar, and Devavrat Shah. Gossip algorithms: Design, analysis and applications. In INFOCOM 2005. 24th Annual
Joint Conference of the IEEE Computer and Communications Societies.
Proceedings IEEE, volume 3, pages 1653-1664. IEEE, 2005.
[24] Mason A Porter, Jukka-Pekka Onnela, and Peter J Mucha. Communities in networks. Notices of the AMS, 56(9):1082-1097, 2009.
[25] Fang Wu and Bernardo A Huberman. Finding communities in linear time: a physics approach. The European Physical Journal B-Condensed Matter and Complex Systems, 38(2):331-338, 2004.
[26] Jordi Duch and Alex Arenas. Community detection in complex networks using
extremal optimization. Physical review E, 72(2):027104, 2005.
[27] Usha Nandini Raghavan, Reka Albert, and Soundar Kumara. Near linear time
algorithm to detect community structures in large-scale networks. Physical Review
E, 76(3):036106, 2007.
[28] Aaron Clauset, Mark EJ Newman, and Cristopher Moore. Finding community structure in very large networks. Physical review E, 70(6):066111, 2004.
[29] Andrea Lancichinetti, Santo Fortunato, and Janos Kertesz. Detecting the overlapping and hierarchical community structure in complex networks. New Journal of Physics, 11(3):033015, 2009.
[30] Inderjit S Dhillon, Yuqiang Guan, and Brian Kulis. Kernel k-means: spectral clustering and normalized cuts. In Proceedings of the tenth ACM SIGKDD international conference on Knowledge discovery and data mining, pages 551-556. ACM, 2004.
[31] Brian Kulis, Sugato Basu, Inderjit Dhillon, and Raymond Mooney. Semi-supervised graph clustering: a kernel approach. Machine Learning, 74(1):1-22, 2009.
[32] Bo Long, Zhongfei Mark Zhang, and Philip S Yu. A probabilistic framework for relational clustering. In Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining, pages 470-479. ACM, 2007.
[33] Brian Karrer and Mark EJ Newman. Stochastic block models and community structure in networks. Physical Review E, 83(1):016107, 2011.
[34] Leon Danon, Albert Diaz-Guilera, Jordi Duch, and Alex Arenas. Comparing community structure identification. Journal of Statistical Mechanics: Theory and Experiment, 2005(09):P09008, 2005.
[35] Andrea Lancichinetti and Santo Fortunato. Community detection algorithms: A
comparative analysis. Physical review E, 80(5):056117, 2009.
[36] Linton C Freeman. A set of measures of centrality based on betweenness. Sociometry, pages 35-41, 1977.
[37] Linton C Freeman. Centrality in social networks conceptual clarification. Social
networks, 1(3):215-239, 1979.
[38] Mark Newman. Networks: an introduction. OUP Oxford, 2009.
[39] Cheng-Shang Chang, Chin-Yi Hsu, Jay Cheng, and Duan-Shin Lee. A general probabilistic framework for detecting community structure in networks. In INFOCOM, 2011 Proceedings IEEE, pages 730-738. IEEE, 2011.
[40] David Liben-Nowell and Jon Kleinberg. The link prediction problem for social networks. In Proceedings of the twelfth international conference on Information and
knowledge management, pages 556-559. ACM, 2003.
[41] Leo Katz. A new status index derived from sociometric analysis. Psychometrika,
18(1):39-43, 1953.
[42] Santo Fortunato and Marc Barthelemy. Resolution limit in community detection.
Proceedings of the National Academy of Sciences, 104(1):36-41, 2007.
[43] Persi Diaconis and Daniel Stroock. Geometric bounds for eigenvalues of markov
chains. The Annals of Applied Probability, 1(1):36-61, 1991.
[44] Daniel A Spielman and Shang-Hua Teng. Nearly-linear time algorithms for graph partitioning, graph sparsification, and solving linear systems. In Proceedings of the thirty-sixth annual ACM symposium on Theory of computing, pages 81-90. ACM,
2004.
[45] Bingying Xu, Zheng Liang, Yan Jia, Bin Zhou, and Yi Han. Local community detection using seeds expansion. In Cloud and Green Computing (CGC), 2012 Second International Conference on, pages 557-562. IEEE, 2012.
[46] Xuan-Chao Huang, Jay Cheng, Hsin-Hung Chou, Chih-Heng Cheng, and Hsien-
Tsan Chen. Detecting overlapping communities in networks based on a simple node
bahavior model. Preprint.
[47] Jorg Reichardt and Stefan Bornholdt. Statistical mechanics of community detection. Physical Review E, 74(1):016110, 2006.
[48] Alex Arenas, Alberto Fernandez, and Sergio Gomez. Analysis of the structure of complex networks at different resolution levels. New Journal of Physics, 10(5):053039,2008.
[49] Wayne W Zachary. An information flow model for conflict and fission in small groups. Journal of anthropological research, pages 452-473, 1977.