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Community Detection and Visualization of Networks with the Map Equation Framework

  • Ludvig Bohlin
  • Daniel Edler
  • Andrea Lancichinetti
  • Martin Rosvall
Chapter

Abstract

Large networks contain plentiful information about the organization of a system. The challenge is to extract useful information buried in the structure of myriad nodes and links. Therefore, powerful tools for simplifying and highlighting important structures in networks are essential for comprehending their organization. Such tools are called community-detection methods and they are designed to identify strongly intraconnected modules that often correspond to important functional units. Here we describe one such method, known as the map equation, and its accompanying algorithms for finding, evaluating, and visualizing the modular organization of networks. The map equation framework is very flexible and can identify two-level, multi-level, and overlapping organization in weighted, directed, and multiplex networks with its search algorithm Infomap. Because the map equation framework operates on the flow induced by the links of a network, it naturally captures flow of ideas and citation flow, and is therefore well-suited for analysis of bibliometric networks.

Keywords

Random Walker Community Detection Module Assignment Huffman Code Network Partition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Aldecoa, R., & Marín, I. (2013). Exploring the limits of community detection strategies in complex networks. Scientific Reports, 3, 2216.Google Scholar
  2. Barrat, A., Barthelemy, M., & Vespignani, A. (2008). Dynamical processes on complex networks (Vol. 574). Cambridge: Cambridge University Press.CrossRefzbMATHGoogle Scholar
  3. Blei, D. M., Ng, A. Y., & Jordan, M. I. (2003). Latent Dirichlet allocation. Journal of Machine Learning Research, 3, 993–1022.zbMATHGoogle Scholar
  4. Blondel, V. D., Guillaume, J. L., Lambiotte, R., & Lefebvre, E. (2008). Fast unfolding of communities in large networks. Journal of Statistical Mechanics: Theory and Experiment, 2008(10), P10008.CrossRefGoogle Scholar
  5. Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., & Hwang, D. U. (2006). Complex networks: Structure and dynamics. Physics Reports, 424(4), 175–308.CrossRefMathSciNetGoogle Scholar
  6. Brin, S., & Page, L. (1998). The anatomy of a large-scale hypertextual Web search engine. Computer Networks and ISDN Systems, 30(1), 107–117.CrossRefGoogle Scholar
  7. Dorogovtsev, S. N., & Mendes, J. F. F. (2003). Evolution of networks: From biological Nets to the Internet and WWW. Oxford: Oxford University Press.CrossRefGoogle Scholar
  8. Esquivel, A. V., & Rosvall, M. (2011). Compression of flow can reveal overlapping-module organization in networks. Physical Review X, 1(2), 021025.CrossRefGoogle Scholar
  9. Fortunato, S. (2010). Community detection in graphs. Physics Reports, 486(3), 75–174.CrossRefMathSciNetGoogle Scholar
  10. Fortunato, S., & Barthelemy, M. (2007). Resolution limit in community detection. Proceedings of the National Academy of Sciences, 104(1), 36–41.CrossRefGoogle Scholar
  11. Golub, G. H., & Van Loan, C. F. (2012). Matrix computations (Vol. 3). Baltimore, MD: JHU Press.Google Scholar
  12. Gopalan, P. K., & Blei, D. M. (2013). Efficient discovery of overlapping communities in massive networks. Proceedings of the National Academy of Sciences, 110(36), 14534–14539.CrossRefzbMATHMathSciNetGoogle Scholar
  13. Huffman, D. A. (1952). A method for the construction of minimum redundancy codes. Proceedings of the IRE, 40(9), 1098–1101.CrossRefGoogle Scholar
  14. Kanungo, T., Mount, D. M., Netanyahu, N. S., Piatko, C. D., Silverman, R., & Wu, A. Y. (2002). An efficient k-means clustering algorithm: Analysis and implementation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 24(7), 881–892.CrossRefGoogle Scholar
  15. Karrer, B., & Newman, M. E. (2011). Stochastic blockmodels and community structure in networks. Physical Review E, 83(1), 016107.CrossRefMathSciNetGoogle Scholar
  16. Kawamoto, T., & Rosvall, M. (2014). The map equation and the resolution limit in community detection. arXiv preprint arXiv:1402.4385.Google Scholar
  17. Lambiotte, R., & Rosvall, M. (2012). Ranking and clustering of nodes in networks with smart teleportation. Physical Review E, 85(5), 056107.CrossRefGoogle Scholar
  18. Lancichinetti, A., & Fortunato, S. (2009). Community detection algorithms: A comparative analysis. Physical Review E, 80(5), 056117.CrossRefGoogle Scholar
  19. Lancichinetti, A., Fortunato, S., & Radicchi, F. (2008). Benchmark graphs for testing community detection algorithms. Physical Review E, 78(4), 046110.CrossRefGoogle Scholar
  20. Lancichinetti, A., Radicchi, F., Ramasco, J. J., & Fortunato, S. (2011). Finding statistically significant communities in networks. PLoS ONE, 6(4), e18961.CrossRefGoogle Scholar
  21. Newman, M. E. (2001). Scientific collaboration networks. II. Shortest paths, weighted networks, and centrality. Physical Review E, 64(1), 016132.CrossRefGoogle Scholar
  22. Newman, M. E. (2003). The structure and function of complex networks. SIAM Review, 45(2), 167–256.CrossRefzbMATHMathSciNetGoogle Scholar
  23. Newman, M. E. (2010). Networks: An introduction. New York, NY: Oxford University Press.CrossRefGoogle Scholar
  24. Newman, M. E., & Girvan, M. (2004). Finding and evaluating community structure in networks. Physical Review E, 69(2), 026113.CrossRefGoogle Scholar
  25. Peixoto, T. P. (2013). Hierarchical block structures and high-resolution model selection in large networks. arXiv preprint arXiv:1310.4377.Google Scholar
  26. Rosvall, M., & Bergstrom, C. T. (2008). Maps of random walks on complex networks reveal community structure. Proceedings of the National Academy of Sciences, 105(4), 1118–1123.CrossRefGoogle Scholar
  27. Rosvall, M., & Bergstrom, C. T. (2010). Mapping change in large networks. PLoS ONE, 5(1), e8694.CrossRefGoogle Scholar
  28. Rosvall, M., & Bergstrom, C. T. (2011). Multilevel compression of random walks on networks reveals hierarchical organization in large integrated systems. PLoS ONE, 6(4), e18209.CrossRefGoogle Scholar
  29. Rosvall, M., Esquivel, A. V., West, J., Lancichinetti, A., & Lambiotte, R. (2013). Memory in network flows and its effects on community detection, ranking, and spreading. arXiv preprint arXiv:1305.4807.Google Scholar
  30. Schaub, M. T., Lambiotte, R., & Barahona, M. (2012). Encoding dynamics for multiscale community detection: Markov time sweeping for the map equation. Physical Review E, 86(2), 026112.CrossRefGoogle Scholar
  31. Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27(3), 379–423.CrossRefzbMATHMathSciNetGoogle Scholar
  32. Traag, V. A., Van Dooren, P., & Nesterov, Y. (2011). Narrow scope for resolution-limit-free community detection. Physical Review E, 84(1), 016114.CrossRefGoogle Scholar
  33. van Dongen, S. M. (2000). Graph clustering by flow simulation. Doctoral dissertation, University of Utrecht, the Netherlands.Google Scholar
  34. Waltman, L., & Eck, N. J. (2012). A new methodology for constructing a publication‐level classification system of science. Journal of the American Society for Information Science and Technology, 63(12), 2378–2392.CrossRefGoogle Scholar
  35. Ward, J. H., Jr. (1963). Hierarchical grouping to optimize an objective function. Journal of the American Statistical Association, 58(301), 236–244.CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Ludvig Bohlin
    • 1
  • Daniel Edler
    • 1
  • Andrea Lancichinetti
    • 1
  • Martin Rosvall
    • 1
  1. 1.Integrated Science Lab, Department of PhysicsUmeå UniversityUmeåSweden

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