Compression of Flow Can Reveal Overlapping-Module Organization in Networks

Physical Review X

Volumn 1, Issue 2, 2011, Pages 1-11

  Esquivel, Alcides Viamontes ^a   Rosvall, Martin ^a  

^a UMEÅ UNIVERSITY   (Sweden)

Author keywords

Complex Systems; Computational Physics; Interdisciplinary Physics

Indexed keywords

CAENORHABDITIS ELEGANS; CAPTURE FLOW; COMPUTATIONAL PHYSICS; GENERALIZED MAP; INTERDISCIPLINARY PHYSICS; LARGE NETWORKS; NETWORK PARTITIONS;

LARGE SCALE SYSTEMS;

INFORMATION THEORY;

EID: 84865130854     PISSN: None     EISSN: 21603308     Source Type: Journal    
DOI: 10.1103/PhysRevX.1.021025     Document Type: Article

References (36)

1. R. Albert and A. L. Barabási, Statistical Mechanics of Complex Networks, Rev. Mod. Phys. 74, 47 (2002).
2. R. Pastor-Satorras and A. Vespignani, Evolution and Structure of the Internet: A Statistical Physics Approach (Cambridge University Press, Cambridge, England, 2004), ISBN 0521826985.
3. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D. U. Hwang, Complex Networks: Structure and Dynamics, Phys. Rep. 424, 175
4. C. Ratti, S. Sobolevsky, F. Calabrese, C. Andris, J. Reades, and O. Sporns, Redrawing the Map of Great Britain from a Network of Human Interactions, PLoS ONE 5, e14248 (2010).
5. R. D. Alba and G. Moore, Elite Social Circles, Sociological Methods and Research 7, 167 (1978).
6. S. Fortunato, Community Detection in Graphs, Phys. Rep. 486, 75 (2010).
7. M. E. J. Newman and M. Girvan, Finding and Evaluating Community Structure in Networks, Phys. Rev. E 69, 026113 (2004).
8. M. E. J. Newman, Fast Algorithm for Detecting Community Structure in Networks, Phys. Rev. E 69, 066133 (2004).
9. D. M. Wilkinson and B. A. Huberman, A Method for Finding Communities of Related Genes, Proc. Natl. Acad. Sci. U.S.A. 101, 5241 (2004).
10. D. Gfeller, J.-C. Chappelier, and P. De Los Rios, Finding Instabilities in the Community Structure of Complex Networks, Phys. Rev. E 72, 056135 (2005).
11. G. Palla, A. L. Barabási, and T. Vicsek, Quantifying Social Group Evolution, Nature (London) 446, 664 (2007).
12. S. Gregory, in Machine Learning and Knowledge Discovery in Databases: Proceedings, Part 1, European Conference, Antwerp, 2008, Lecture Notes in Computer Science: Lecture Notes in Artificial Intelligence, Vol. 5211, edited by W. Daelemans and K. Morik (Springer, New York, 2008), pp. 408-423.
13. Andrea Lancichinetti, Filippo Radicchi, José J. Ramasco, and Santo Fortunato, Finding Statistically Significant Communities in Networks, PLoS ONE 6, e18961 (2011).
14. J. Whitney, J. Koh, M. Costanzo, G. Brown, C. Boone, and M. Brudno, in Proceedings of the 11th International Conference on Algorithms in Bioinformatics. Lecture Notes in Computer Science: Lecture Notes in Bioinformatics, edited by T. M. Przytycka and M.-F. Sagot (Springer-Verlag, Berlin, 2011), pp. 326-338.
15. T. S. Evans and R. Lambiotte, Line Graphs, Link Partitions, and Overlapping Communities, Phys. Rev. E 80, 016105
16. Yong-Yeol Ahn, James P. Bagrow, and Sune Lehmann, Link Communities Reveal Multiscale Complexity in Networks, Nature (London) 466, 761 (2010).
17. Y. Kim and H. Jeong, Map Equation for Link Communities, Phys. Rev. E 84. 026110 (2011).
18. M. Rosvall, D. Axelsson, and Carl T. Bergstrom, The Map Equation, Eur. Phys. J. Special Topics 178, 13 (2009).
19. M. Rosvall and Carl T. Bergstrom, Maps of Information Flow Reveal Community Structure in Complex Networks, Proc. Natl. Acad. Sci. U.S.A. 105, 1118 (2008).
20. P. D. Grünwald, The Minimum Description Length Principle (MIT, Cambridge, MA, 2007), ISBN 0262072815.
21. C. E. Shannon and W. Weaver, The Mathematical Theory of Communication (University of Illinois, Champaign, IL, 1949).
22. See http://www.mapequation.org.
23. Martin Rosvall and Carl T. Bergstrom Multilevel Compression of Random Walks on Networks Reveals Hierarchical Organization in Large Integrated Systems, PLoS ONE 6, e18209
24. M. E. J. Newman, The Structure and Function of Complex Networks, SIAM Rev. 45, 167 (2003).
25. We compiled the road-network data from this source in 2010: http://europe.aaroads.com/eroads/erdlist.htm.
26. D. J. Watts and S. H. Strogatz, Collective Dynamics of 'Small-World' Networks, Nature (London) 393, 440 (1998).
27. K. I. Goh, M. E. Cusick, D. Valle, B. Childs, M. Vidal, and A. L. Barabási, The Human Disease Network, Proc. Natl. Acad. Sci. U.S.A. 104, 8685 (2007).
28. We compiled the network in 2010 based on the coauthorships in Refs. .
29. R. Guimera, S. Mossa, A. Turtschi, and L. A. N. Amaral, The Worldwide Air Transportation Network: Anomalous Centrality, Community Structure, and Cities' Global Roles, Proc. Natl. Acad. Sci. U.S.A. 102, 7794 (2005).
30. L. A. Adamic and N. Glance, in Proceedings of the 3rd International Workshop on Link Discovery, 2005 (Association for Computing Machinery, New York, 2005), pp. 36-43, ISBN 1595932151 [http://dl.acm.org/ citation.cfm?id=1134271].
31. We compiled the network in 2010 from data provided by http://www.Twingly.com.
32. G. Palla, I. Derényi, I. Farkas, and T. Vicsek, Uncovering the Overlapping Community Structure of Complex Networks in Nature and Society, Nature (London) 435, 814 (2005).
33. A. Lancichinetti and S. Fortunato, Benchmarks for Testing Community Detection Algorithms on Directed and Weighted Graphs with Overlapping Communities, Phys. Rev. E 80, 016118 (2009).
34. S. Brin and L. Page, The Anatomy of a Large-Scale Hypertextual Web Search Engine, Computer Networks and ISDN Systems 30, 107 (1998).
35. H. A. van der Vorst, Bi-cgstab: A Fast and Smoothly Converging Variant of bi-cg for the Solution of Nonsymmetric Linear Systems, SIAM J. Sci. Comput. 13, 631 (1991).
36. See https://sites.google.com/site/alcidesve82/ for the code.