复杂网络可视化与Link OLAP
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摘要
复杂网络的结构非常复杂，如果仅用数据表格或文字的形式来表示网络，理解起来非常困难，导致网络所包含的信息无从体现。将复杂网络方便、直观地表示出来的最好方法是将其进行可视化，其相关研究涉及复杂系统、图论、统计学、数据挖掘、信息可视化以及人机交互等多个领域。
数据仓库与OLAP系统经过长期的发展，目前在逻辑模型、物理模型以及展现方式上都已经有了一套完整的理论与技术体系。但传统的OLAP系统有其特定的关注点，并一定程度上存在局限性，为此我们提出了一个新的OLAP概念——Link OLAP。
本文综合探讨以上两方面技术。首先在综述复杂网络可视化研究的基础上，我们总结并提出若干处理复杂网络可视化的关键技术，同时对其实现细节进行探讨。而后我们将重点放在新的OLAP概念体系——Link OLAP的讨论上，通过将面向实体的分析扩展到面向链接的分析，Link OLAP在某些特定的分析场景下能够提供比传统OLAP更为优雅的解决方案，其应用领域是存在大量基于链接信息的复杂网络或大规模数据网络。以复杂网络可视化技术为基础，Link OLAP系统突破了以往传统OLAP系统中单调的二维表格表现方式，能够提供友好的交互式可视化用户接口。此外，我们还详细地给出了Link OLAP系统的一个示例实现，从系统架构设计到底层实现的各个层面都会有所涉及，并对其中的若干核心模块进行深入探讨。最后我们以一个实际案例来说明Link OLAP概念系统的应用效果。
Complex Network is so complicated that if we only use data table or text to express it, the network will be hard to understand and the contained information could not be revealed. The best way to express complex network is visualization whose related research areas involve complex system, graph theory, statistics, data mining, information visualization and human-machine conversation.
After long period of development, data warehouse and OLAP have already had an integrated system of theory and technology in logical model, physical model and visualization. Since there are specific observational points and some limited factors in traditional OLAP, we present a new OLAP concept: Link OLAP.
This paper discusses the above two technologies. At first, base on the survey of complex network visualization we summarize and present some of its key technologies, and also probe into some implementation details. Then we focus on discussing the new OLAP concept - Link OLAP. Via expanding the entity-oriented analysis into link-oriented analysis, Link OLAP could solve problems more refinedly than traditional OLAP under certain scenarios, including complex network or large scale network contained a mass of links. Base on complex network visualization technology, Link OLAP could provide a friendly interactive visualization user interface, rather than the planar table representation of traditional OLAP. Furthermore, we also give a sample implementation of Link OLAP system in detail, which includes architecture design, bottom layer implementation and some core module analysis. At last, we explain the practical effect of Link OLAP system using an application demo.
数据仓库与OLAP系统经过长期的发展，目前在逻辑模型、物理模型以及展现方式上都已经有了一套完整的理论与技术体系。但传统的OLAP系统有其特定的关注点，并一定程度上存在局限性，为此我们提出了一个新的OLAP概念——Link OLAP。
本文综合探讨以上两方面技术。首先在综述复杂网络可视化研究的基础上，我们总结并提出若干处理复杂网络可视化的关键技术，同时对其实现细节进行探讨。而后我们将重点放在新的OLAP概念体系——Link OLAP的讨论上，通过将面向实体的分析扩展到面向链接的分析，Link OLAP在某些特定的分析场景下能够提供比传统OLAP更为优雅的解决方案，其应用领域是存在大量基于链接信息的复杂网络或大规模数据网络。以复杂网络可视化技术为基础，Link OLAP系统突破了以往传统OLAP系统中单调的二维表格表现方式，能够提供友好的交互式可视化用户接口。此外，我们还详细地给出了Link OLAP系统的一个示例实现，从系统架构设计到底层实现的各个层面都会有所涉及，并对其中的若干核心模块进行深入探讨。最后我们以一个实际案例来说明Link OLAP概念系统的应用效果。
Complex Network is so complicated that if we only use data table or text to express it, the network will be hard to understand and the contained information could not be revealed. The best way to express complex network is visualization whose related research areas involve complex system, graph theory, statistics, data mining, information visualization and human-machine conversation.
After long period of development, data warehouse and OLAP have already had an integrated system of theory and technology in logical model, physical model and visualization. Since there are specific observational points and some limited factors in traditional OLAP, we present a new OLAP concept: Link OLAP.
This paper discusses the above two technologies. At first, base on the survey of complex network visualization we summarize and present some of its key technologies, and also probe into some implementation details. Then we focus on discussing the new OLAP concept - Link OLAP. Via expanding the entity-oriented analysis into link-oriented analysis, Link OLAP could solve problems more refinedly than traditional OLAP under certain scenarios, including complex network or large scale network contained a mass of links. Base on complex network visualization technology, Link OLAP could provide a friendly interactive visualization user interface, rather than the planar table representation of traditional OLAP. Furthermore, we also give a sample implementation of Link OLAP system in detail, which includes architecture design, bottom layer implementation and some core module analysis. At last, we explain the practical effect of Link OLAP system using an application demo.
引文
1 http://www.ads.tuwien.ac.at/AGD/
2 http://jung.sourceforge.net/
3 http://www.graphviz.org/
4 http://vlado.fmf:uni-lj.si/pub/networks/pajek/
5 http://www.cs.umd.edu/hcil/piccolo/
6 http://www.analytictech.com/ucinet.htm
7 http://www.dia.uniroma3.it/～gdt/
8 http://ivtk.sourceforge.net/
9 http://www.cs.sandia.gov/projects/VxInsight.html
10 http://www.touchgraph.com/
11 http://whatsonweb.diei.unipg.it/
12 http://www.friendster.com/
[1] Wang XY, Zhou AY. Linkage analysis for the World Wide Web and its application: A survey. Journal of Software, 2003,14(10): 1768～1780.(王晓宇，周傲英，万维网的链接结构分析及其应用综述，软件学报，2003，14(10)：1768～1780．)
[2] Barabasi, Albert-Laszlo; Bonabeau, Eric, Scale-free networks. Scientific American 288, 2003, 60-69. 1,2
[3] D. J. Watts and S. H. Strogatz. Collective dynamics of'smallworld ' networks. In Natm'e, vol. 393, pp. 440-442, 1998.
[4] Adel Ahmed, Tim Dywer, Seok-Hee Hong, Colin Murray, Le Song and Ying Xin Wu, Visualisation and Analysis of Large and Complex Scale-free Networks, EUROGRAPHICS-IEEE VGTC Symposium on Visualization (2005), pp. 1-8.
[5] P. Eades, A heuristic for graph drawing, Congressus Nutnerantiunt, 42, 149-160 (1984).
[6] G. D. Battista, P. Eades, R. Tamassia, I. G. Tollis, "Algorithms for Drawing Graphs: an Annotated Bibliography", Computational Geometry: Theory and Applications, 1994, 4(5), 235-282.
[7] T. M. J. Fruchterman, E. M. Reingold, "Graph Drawing by Force-Directed Placement", Software-Practice and Experience, 1991, vol. 21, no. 11, 1129-1164.
[8] HUANG Jing-wei, KANG Li-shan, CHEN Yu-ping, A New Graph Drawing Algorithm for Undirected Graphs, Journal of Software, 2000,11(1): 138-142. (黄竞伟，康立山，陈毓屏，“一个新的无向图画图算法”，软件学报，2000，11(1)，138-142．)
[9] F. van Ham, J. J. van Wijk, "Interactive Visualization of Small World Graphs", Proceedings of the IEEE Symposium on Information Visualization (INFOVIS'04), 2004, Volume 00, 199-206.
[10] David Harel and Yehuda Koren. A fast multi-scale method for drawing large graphs. In Graph Drawing: 8th International Symposium (GD'00), pages 183-196,2000.
[11] Aaron Quigley and Peter Eades. Graph drawing, clustering, and visual abstraction. In Joe Marks, editor, Proc. 8th Int. Symp. Graph Drawing, pages 197-210. Springer LNCS 1984, 2000.
[12] C.Walshaw. A multilevel algorithm for force-directed graph drawing. In Joe Marks, editor, Proc. 8th Int. Symp. Graph Drawing, pages 171-182. Springer-Verlag, 2000.
[13] P. Gajer, M. Goodrich, and S. Kobourov. A multi-dimensional approach to force-directed layouts of large graphs. In Joe Marks, editor, Proc. 8th Int. Symp. on Graph Drawing, pages 211-221. Springer-Verlag, 2000.
[14] A. Noack. An energy model for visual graph clustering. In Proc. 11th Int. Symp. on Graph Drawing, pages 425-436. Springer-Verlag, 2003.
[15] T. Kamada, S. Kawai, "An Algorithm for Drawing General Undirected Graphs", Information Processing Letters, 1989, vol. 31, 7-15.
[16] D. Chan, K. Chua, C. Leckie and A. Parhar. "Visualisation of Power-Law Network Topologies." In Proceedings of the Eleventh IEEE International Conference on Networks (ICON 2003), 28 September - 1 October 2003, Sydney, Australia, pp. 69-74.
[17] J. Winick and S. Jamin. Inet-3.0: Internet topology generator. Technical Report CSE-TR-456-02, University of Michigan, 2002.
[18] WARE C: Designing with a 2 l/2d attitude. Information Design Journal 10, 3 (2001), 171-182.
[19] Agrawa 1R, Imielinski T, Swami A. Mining association rules between sets of items in large databases (C). In: Buneman P, Jajodia S,eds. Proc. of the ACM SIGMOD Conf. on Management of Data (SIGMOD'93). New York: ACM Press, 1993.207-216.
[20] QUIGLEY A., EADES P.: Fade: Graph drawing, clustering, and visual abstraction. In Proceedings of International Symposium on Graph Drawing (GD2000) (2000), vol. 1984, Springer, pp. 197-210.
[21] GAJER P., GOODRICH M., KOBOUROV S.: A multi-dimensional approach to force-directed drawings of large graphs. In Proceedings of International Symposium on Graph Drawing (GD2000) (2000), vol. 1984, Springer, pp. 211-221.
[22] HAREL D., KOREN Y.: Graph drawing by high-dimensional embedding. In Proceedings of International Symposium on Graph Drawing (GD2002) (2002), vol. 2528, Springer, pp. 207-2191.
[23] KOREN Y., CARMEL L., HAREL D.: Ace: A fast multiscale eigenvectors computation for drawing huge graphs. In Proceedings of the IEEE Symposium on Information Visualisation 2002 (2002), pp. 137-144.
[24] WILLIAMS M., MUNZNER T.: Steerable, progressive multidimensional scaling. In Proceedings of the IEEE Symposium on Information Visualisation 2004 (2004), pp. 57-64.
[25] DUKE D.: Visual web mining. In Proceedings of the 13th International World Wide Web conferenece on Alternate track papers & posters (2004), pp. 394-395.
[26] MORRISON A., CHALMERS M.: Improving hybrid rods with pivot-based searching. In Proceedings of the IEEE Symposium on Information Visualisation 2003 (2003), pp. 85-90.
[27] ZHANG Qing-guo, HUANG Jing-wei, A Algorithm for Drawing Undirected Planar Graph, MINI-MICRO SYSTEMS, 2003, vol.24, No.6, 972-975.(张清国，黄竞伟，一个无向平面图的画图算法，小型微型计算机系统，2003，Vol．24，No．6，pp．972-975．)
[28] A. C. Gilbert and K. Levchenko, Compressing network graphs, LINKKDD2004.
[29] T. Feder and R. Motwani. Clique partitions, graph compression and speeding-up algorithms. Journal of Computer And System Sciences, 51:261-272, 1995.
[30] M. Adler and M. Mitzenmacher. Towards compressing web graphs. In Proceedings of the IEEE Data Compression Conference, pages 203-212, 2001.
[31] Emden Gansner, Yehuda Koren, Stephen North, Topological Fisheye Views for Visualizing Large Graphs, IEEE Transactions on Visualization and Computer Graphics, 2005, Volume 11, Issue 4, pp.457 - 468.
[32] Soon Tee Teoh, Ke Zhang, Shih-Ming Tseng, Kwan-Liu Ma and S.Felix Wu. Combining Visual and Automated Data Mining for Near-Real-Time Anomaly Detection and Analysis in BGP. VizSEC/DMSEC'04, October 29, 2004
[33] R.F.Erbacher, K.L.Walker, and D.A.Fincke. Intrusion and misuse Detection in Large-Scale System, IEEE Computer Graphics and Applications, Vol, 22, no,1, Jan.Feb. 2002,pp.38-48
[34] Kofi Nyarko, Tanya Capers, Craig Scott, Kemi Ladeji-Osias .Network Intrusion Visualization with NIVA, an Intrusion Detection Visual Analyzer with Haptic Integration. Proceeding of the 10th Symp, (HAPTICS'02) 2002 IEEE
[35] Johnathan Ishmael, Nicholas J.P.Race .Visawin: Visualizing a Wireless Network. 0-7803-8255-2/04 IEEE,2004
[36] Robert F. Erbacher, Kim Christensen, and Amanda Sundberg. Designing Visualization Capabilities for IDS Challenges
[37] Freeman. L.Visualizing Social Networks. Journal of Social Structure, 2000, 1
[38] Jeffrey Heer, danah boyd. Vizster: Visualiziing Online Social Networks, 2005
[39] David Liben-Nowell, Jon Kleinberg.The Link Prediction Problem for Social Networks, Proceedings of the Twelfth Annual ACM International Conference on Information and Knowledge Management(CIKM'03), November 2003,pp.556-559
[40] Hsinchun Chen, Homa Atabakhsh, Chunju Tseng, Byron Marshall, Siddharth Kaza, Shauna Eggers, Hemanth Gowda, Ankit Shah Tim Petersen, Chuck Violette. Visualization in Law Enforcenment, CHI 2005, April 2-7
[41] GeNetViz- Gene Network Visualization. http://genetviz.sourceforge.net/, 2005
[42] Shandar Ahmad, Michael M.Gromiha. Prediction of DNA Binding in Proteins from Composition, Sequence and Structure, Genome Informatics 13: 308-309(2002)
[43] Roded Sharan, Adi Maron-Katz and Ron Shamir. CLICK and EXPANDER:a system for clustering and visualizing gene expression data, Bioinformatics 19(14) Oxford University Press 2003
[44] Joshua E. Barnes and Pier Hut. A hierarchical o(n log n) force calculation algorithm. In Nature, volume 324(4), pages 446-449, 1986.
[45] Aaron Quigley and Peter Eades. Graph drawing, clustering, and visual abstraction. In Joe Marks, editor, Proc. 8th Int. Symp. Graph Drawing, pages 197-210. Springer LNCS 1984, 2000.
[46] M.E.J. Newman. Fast algorithm for detecting community structure in networks. Phys. Rev. E (in press), 2004.
[47] Mohammad Ghoniem, Jean-Daniel Fekete, and Philippe Castagliola, A comparison of the readability of graphs using node-link and matrix-based representations, INFOVIS '04: Proceedings of the IEEE Symposium on Information Visualization (INFOVIS'04) (Washington, DC, USA), IEEE Computer Society, 2004, pp. 17-24.
[48] H. C. Purchase, R. F. Cohen, and M. I. James, An experimental study of the basis for graph drawing algorithms, J. Exp. Algorithmics 2 (1997), 4.
[49] U. Brandes, M. Eiglsperger, I. Herman, M. Himsolt, and M.S. Marshall: GraphML Progress Report: Structural Layer Proposal. Proc. 9th Intl. Symp. Graph Drawing (GD '01), LNCS 2265, pp. 501-512. Springer-Verlag, 2002.
[50] Wu Andrew Y.; Garland Michael; Han Jiawei, Mining scale-free networks using geodesic clustering, KDD2004, p 719-724.
2 http://jung.sourceforge.net/
3 http://www.graphviz.org/
4 http://vlado.fmf:uni-lj.si/pub/networks/pajek/
5 http://www.cs.umd.edu/hcil/piccolo/
6 http://www.analytictech.com/ucinet.htm
7 http://www.dia.uniroma3.it/～gdt/
8 http://ivtk.sourceforge.net/
9 http://www.cs.sandia.gov/projects/VxInsight.html
10 http://www.touchgraph.com/
11 http://whatsonweb.diei.unipg.it/
12 http://www.friendster.com/
[1] Wang XY, Zhou AY. Linkage analysis for the World Wide Web and its application: A survey. Journal of Software, 2003,14(10): 1768～1780.(王晓宇，周傲英，万维网的链接结构分析及其应用综述，软件学报，2003，14(10)：1768～1780．)
[2] Barabasi, Albert-Laszlo; Bonabeau, Eric, Scale-free networks. Scientific American 288, 2003, 60-69. 1,2
[3] D. J. Watts and S. H. Strogatz. Collective dynamics of'smallworld ' networks. In Natm'e, vol. 393, pp. 440-442, 1998.
[4] Adel Ahmed, Tim Dywer, Seok-Hee Hong, Colin Murray, Le Song and Ying Xin Wu, Visualisation and Analysis of Large and Complex Scale-free Networks, EUROGRAPHICS-IEEE VGTC Symposium on Visualization (2005), pp. 1-8.
[5] P. Eades, A heuristic for graph drawing, Congressus Nutnerantiunt, 42, 149-160 (1984).
[6] G. D. Battista, P. Eades, R. Tamassia, I. G. Tollis, "Algorithms for Drawing Graphs: an Annotated Bibliography", Computational Geometry: Theory and Applications, 1994, 4(5), 235-282.
[7] T. M. J. Fruchterman, E. M. Reingold, "Graph Drawing by Force-Directed Placement", Software-Practice and Experience, 1991, vol. 21, no. 11, 1129-1164.
[8] HUANG Jing-wei, KANG Li-shan, CHEN Yu-ping, A New Graph Drawing Algorithm for Undirected Graphs, Journal of Software, 2000,11(1): 138-142. (黄竞伟，康立山，陈毓屏，“一个新的无向图画图算法”，软件学报，2000，11(1)，138-142．)
[9] F. van Ham, J. J. van Wijk, "Interactive Visualization of Small World Graphs", Proceedings of the IEEE Symposium on Information Visualization (INFOVIS'04), 2004, Volume 00, 199-206.
[10] David Harel and Yehuda Koren. A fast multi-scale method for drawing large graphs. In Graph Drawing: 8th International Symposium (GD'00), pages 183-196,2000.
[11] Aaron Quigley and Peter Eades. Graph drawing, clustering, and visual abstraction. In Joe Marks, editor, Proc. 8th Int. Symp. Graph Drawing, pages 197-210. Springer LNCS 1984, 2000.
[12] C.Walshaw. A multilevel algorithm for force-directed graph drawing. In Joe Marks, editor, Proc. 8th Int. Symp. Graph Drawing, pages 171-182. Springer-Verlag, 2000.
[13] P. Gajer, M. Goodrich, and S. Kobourov. A multi-dimensional approach to force-directed layouts of large graphs. In Joe Marks, editor, Proc. 8th Int. Symp. on Graph Drawing, pages 211-221. Springer-Verlag, 2000.
[14] A. Noack. An energy model for visual graph clustering. In Proc. 11th Int. Symp. on Graph Drawing, pages 425-436. Springer-Verlag, 2003.
[15] T. Kamada, S. Kawai, "An Algorithm for Drawing General Undirected Graphs", Information Processing Letters, 1989, vol. 31, 7-15.
[16] D. Chan, K. Chua, C. Leckie and A. Parhar. "Visualisation of Power-Law Network Topologies." In Proceedings of the Eleventh IEEE International Conference on Networks (ICON 2003), 28 September - 1 October 2003, Sydney, Australia, pp. 69-74.
[17] J. Winick and S. Jamin. Inet-3.0: Internet topology generator. Technical Report CSE-TR-456-02, University of Michigan, 2002.
[18] WARE C: Designing with a 2 l/2d attitude. Information Design Journal 10, 3 (2001), 171-182.
[19] Agrawa 1R, Imielinski T, Swami A. Mining association rules between sets of items in large databases (C). In: Buneman P, Jajodia S,eds. Proc. of the ACM SIGMOD Conf. on Management of Data (SIGMOD'93). New York: ACM Press, 1993.207-216.
[20] QUIGLEY A., EADES P.: Fade: Graph drawing, clustering, and visual abstraction. In Proceedings of International Symposium on Graph Drawing (GD2000) (2000), vol. 1984, Springer, pp. 197-210.
[21] GAJER P., GOODRICH M., KOBOUROV S.: A multi-dimensional approach to force-directed drawings of large graphs. In Proceedings of International Symposium on Graph Drawing (GD2000) (2000), vol. 1984, Springer, pp. 211-221.
[22] HAREL D., KOREN Y.: Graph drawing by high-dimensional embedding. In Proceedings of International Symposium on Graph Drawing (GD2002) (2002), vol. 2528, Springer, pp. 207-2191.
[23] KOREN Y., CARMEL L., HAREL D.: Ace: A fast multiscale eigenvectors computation for drawing huge graphs. In Proceedings of the IEEE Symposium on Information Visualisation 2002 (2002), pp. 137-144.
[24] WILLIAMS M., MUNZNER T.: Steerable, progressive multidimensional scaling. In Proceedings of the IEEE Symposium on Information Visualisation 2004 (2004), pp. 57-64.
[25] DUKE D.: Visual web mining. In Proceedings of the 13th International World Wide Web conferenece on Alternate track papers & posters (2004), pp. 394-395.
[26] MORRISON A., CHALMERS M.: Improving hybrid rods with pivot-based searching. In Proceedings of the IEEE Symposium on Information Visualisation 2003 (2003), pp. 85-90.
[27] ZHANG Qing-guo, HUANG Jing-wei, A Algorithm for Drawing Undirected Planar Graph, MINI-MICRO SYSTEMS, 2003, vol.24, No.6, 972-975.(张清国，黄竞伟，一个无向平面图的画图算法，小型微型计算机系统，2003，Vol．24，No．6，pp．972-975．)
[28] A. C. Gilbert and K. Levchenko, Compressing network graphs, LINKKDD2004.
[29] T. Feder and R. Motwani. Clique partitions, graph compression and speeding-up algorithms. Journal of Computer And System Sciences, 51:261-272, 1995.
[30] M. Adler and M. Mitzenmacher. Towards compressing web graphs. In Proceedings of the IEEE Data Compression Conference, pages 203-212, 2001.
[31] Emden Gansner, Yehuda Koren, Stephen North, Topological Fisheye Views for Visualizing Large Graphs, IEEE Transactions on Visualization and Computer Graphics, 2005, Volume 11, Issue 4, pp.457 - 468.
[32] Soon Tee Teoh, Ke Zhang, Shih-Ming Tseng, Kwan-Liu Ma and S.Felix Wu. Combining Visual and Automated Data Mining for Near-Real-Time Anomaly Detection and Analysis in BGP. VizSEC/DMSEC'04, October 29, 2004
[33] R.F.Erbacher, K.L.Walker, and D.A.Fincke. Intrusion and misuse Detection in Large-Scale System, IEEE Computer Graphics and Applications, Vol, 22, no,1, Jan.Feb. 2002,pp.38-48
[34] Kofi Nyarko, Tanya Capers, Craig Scott, Kemi Ladeji-Osias .Network Intrusion Visualization with NIVA, an Intrusion Detection Visual Analyzer with Haptic Integration. Proceeding of the 10th Symp, (HAPTICS'02) 2002 IEEE
[35] Johnathan Ishmael, Nicholas J.P.Race .Visawin: Visualizing a Wireless Network. 0-7803-8255-2/04 IEEE,2004
[36] Robert F. Erbacher, Kim Christensen, and Amanda Sundberg. Designing Visualization Capabilities for IDS Challenges
[37] Freeman. L.Visualizing Social Networks. Journal of Social Structure, 2000, 1
[38] Jeffrey Heer, danah boyd. Vizster: Visualiziing Online Social Networks, 2005
[39] David Liben-Nowell, Jon Kleinberg.The Link Prediction Problem for Social Networks, Proceedings of the Twelfth Annual ACM International Conference on Information and Knowledge Management(CIKM'03), November 2003,pp.556-559
[40] Hsinchun Chen, Homa Atabakhsh, Chunju Tseng, Byron Marshall, Siddharth Kaza, Shauna Eggers, Hemanth Gowda, Ankit Shah Tim Petersen, Chuck Violette. Visualization in Law Enforcenment, CHI 2005, April 2-7
[41] GeNetViz- Gene Network Visualization. http://genetviz.sourceforge.net/, 2005
[42] Shandar Ahmad, Michael M.Gromiha. Prediction of DNA Binding in Proteins from Composition, Sequence and Structure, Genome Informatics 13: 308-309(2002)
[43] Roded Sharan, Adi Maron-Katz and Ron Shamir. CLICK and EXPANDER:a system for clustering and visualizing gene expression data, Bioinformatics 19(14) Oxford University Press 2003
[44] Joshua E. Barnes and Pier Hut. A hierarchical o(n log n) force calculation algorithm. In Nature, volume 324(4), pages 446-449, 1986.
[45] Aaron Quigley and Peter Eades. Graph drawing, clustering, and visual abstraction. In Joe Marks, editor, Proc. 8th Int. Symp. Graph Drawing, pages 197-210. Springer LNCS 1984, 2000.
[46] M.E.J. Newman. Fast algorithm for detecting community structure in networks. Phys. Rev. E (in press), 2004.
[47] Mohammad Ghoniem, Jean-Daniel Fekete, and Philippe Castagliola, A comparison of the readability of graphs using node-link and matrix-based representations, INFOVIS '04: Proceedings of the IEEE Symposium on Information Visualization (INFOVIS'04) (Washington, DC, USA), IEEE Computer Society, 2004, pp. 17-24.
[48] H. C. Purchase, R. F. Cohen, and M. I. James, An experimental study of the basis for graph drawing algorithms, J. Exp. Algorithmics 2 (1997), 4.
[49] U. Brandes, M. Eiglsperger, I. Herman, M. Himsolt, and M.S. Marshall: GraphML Progress Report: Structural Layer Proposal. Proc. 9th Intl. Symp. Graph Drawing (GD '01), LNCS 2265, pp. 501-512. Springer-Verlag, 2002.
[50] Wu Andrew Y.; Garland Michael; Han Jiawei, Mining scale-free networks using geodesic clustering, KDD2004, p 719-724.