Community structures of networks

Mathematics in Computer Science

Volumn 1, Issue 3, 2008, Pages 441-457

  Chen, William Y C ^a   Dress, Andreas W M ^b,c   Yu, Winking Q ^a  

^a NANKAI UNIVERSITY   (China)

^b Chinese Academy of Sciences   (China)

^c MAX PLANCK INSTITUTE FOR MATHEMATICS IN THE SCIENCES   (Germany)

Author keywords

Clique partitioning problem; Community structures; Food webs; Graph partitioning problem; Graphs; Integer linear programming; Linear programming; Networks; Zachary's karate club

Indexed keywords

EID: 49449107396     PISSN: 16618270     EISSN: 16618289     Source Type: Journal    
DOI: 10.1007/s11786-007-0035-1     Document Type: Article

References (36)

1. R. Albert, H. Jeong, and A.-L. Barabási, Diameter of the World-Wide Web. Nature 401, 130-131 (1999).
2. L. A. N. Amaral, A. Scala, M. Barthélémy and H. E. Stanley, Classes of small-world networks. Proc. Natl. Acad. Sci. USA 97, 11149-11152 (2000).
3. J. P. Bagrow and E.M. Bollt, Local method for detecting communities. Phys. Rev. E 72, 046108 (2005).
4. D. Baird and R. E. Ulanowicz, The seasonal dynamics of the Chesapeake Bay ecosystem. Ecological Monographs 59, 329-364 (1989).
5. A.-L. Barabási and R. Albert, Emergence of scaling in random networks. Science 286, 509-512 (1999).
6. C. Bondavalli and R. Ulanowicz, email communication (2006).
7. K.-H. Borgwardt, Untersuchungen zur Asymptotik der mittleren Schriftzahl von Simplexverfahren in der linearen Optimierung. Dissertation, Universität, Kaiserlautern (1977).
8. K.-H. Borgwardt, Some distribution-independent results about the asymptotic order of the average number of pivot steps of the simplex method. Math. Oper. Res. 7, 441-462 (1982).
9. K.-H. Borgwardt, The average number of steps required by the simplex method is polynomial. Zeitschrift für Operations Research 26, 157-177 (1982).
10. K.-H. Borgwardt, Average behavior of the simplex algorithm: Some improvements in the analysis of the rotation-symmetry-model. The 12th Symposium on Mathematical Programming, Cambridge, Mass.
11. I. Charon, L. Denoeud, A. Guénoche and O. Hudry, Maximum transfer distace between partitions. J. Classif. 23 (1), 103-121 (2006).
12. W. Y. C. Chen, A. W. M. Dress, and W. Q. Yu, Checking the reliability of a new approach towards detecting community structures in networks using linear programming. IET Sys. Biol. 5, 286-291 (2007).
13. A. Clauset, Finding local community structure in networks. Phys. Rev. E 72, 026132 (2005).
14. A. Clauset, M. E. J. Newman, and C. Moore, Finding community structure in very large networks, Phys. Rev. E 69, 026113 (2004).
15. G. W. Flake, S. R. Lawrence, C. L. Giles, and F. M. Coetzee, Self-organization and identification of Web communities. IEEE Computer 35, 66-71 (2002).
16. M. Girvan and M. E. J. Newman, Community structure in social and biological networks. Proc. Natl. Acad. Sci. USA 99, 7821-7826 (2002).
17. M. Grötschel, Y. Wakabayashi, A cutting plane algorithm for a clustering problem. Mathematical Programming 45, 59-96 (1989).
18. M. Grötschel, Y. Wakabayashi, Facets of the Clique Partitioning Polytope. Mathematical Programming 47, 367-387 (1990).
19. G. Karypis and V. Kumar, Multilevel k-way partitioning scheme for irregular graphs. Journal of Parallel and Distributed Computing 48(1), 96-129 (1998).
20. G. Karypis and V. Kumar, A fast and highly quality multilevel scheme for partitioning irregular graphs. SIAM J. Sci. Comput. 20(1), 359-392 (1998).
21. B. W. Kernighan and S. Lin, An efficient heuristic procedure for partitioning graphs. Bell System Technical Journal 49, 291-307 (1970).
22. M. E. Newman, Fast algorithm for detecting community structure in networks. Phys. Rev. E 69, 066133 (2004).
23. M. E. J. Newman and M. Girvan, Finding and evaluating community structure in networks, Phys. Rev. E 69, 026113 (2004).
24. A. Pocklington, M. Cumiskey, J. Armstrong and S. Grant, The proteomes of neurotransmitter receptor complexes form modular networks with distributed functionality underlying plasticity and behaviour. Molecular System Biology doi: 10.1038/msb4100041, (2006).
25. A. Pothen, H. Simon, and K.-P. Liou, Partitioning sparse matrices with eigenvectors of graphs. SIAM J. Matrix Anal. Appl. 11, 430-452 (1990).
26. F. Radicchi, C. Castellano, F. Cecconi, V. Loreto and D. Parisi, Defining and idetifying communities in networks. Proc. Natl. Acad. Sci. USA 101, 2658-2663 (2004).
27. J. Reichardt and S. Bornholdt, Detecting fuzzy community structures in complex networks with a Potts model, Phys. Rev. Lett. 93, 218701 (2004).
28. S. Smale, The problem of the average speed of the simplex method. In A. Bachem, M. Grötschel and B. Korte (eds.), Mathematical programming: The state of the art, 530-539. Springer-Verlag, Berlin.
29. J. R. Tyler, D. M. Wilkinson, and B. A. Huberman, Email as spectroscopy : Automated discovery of community structure within organizations. In M. Huysman, E. Wenger, and V. Wulf (eds.), Proceedings of the First International Conference on Communities and Technologies, Kluwer, Dordrecht (2003).
30. R. Ulanowicz, Quantitative methods for ecological network analysis. Comput. Biol. Chem. 28, 321-339 (2004).
31. University of Maryland Center for Environmental Science, Chesapeake Biological Laboratory. http://www.cbl.umces.edu/~atlss/ATLSS.html, accessed November 2006.
32. S. Wasserman and K. Faust, Social network analysis. Cambridge University Press, Cambridge (1994).
33. D. J. Watts and S. H. Strogatz, Collective dynamics of 'small world' networks. Nature 393, 440-442 (1998).
34. Website of METIS, developed by George Karypis, Department of Computer Science & Engineering, University of Minnesota. http://glaros.dtc.umn.edu/ gkhome/metis/metis/download, accessed March 2007.
35. F. Wu and B. A. Huberman, Finding communities in linear time: A physics approach. Eur. Phys. J. B 38, 331-338 (2004).
36. W. W. Zachary, An information flow model for conflict and fisson in small groups. Journal of Anthropological Research 33, 452-473 (1977).