Hostname: page-component-848d4c4894-8bljj Total loading time: 0 Render date: 2024-06-30T03:40:51.646Z Has data issue: false hasContentIssue false
  • English
  • Français

Comparison of algorithms in graph partitioning

Published online by Cambridge University Press:  04 April 2009

Alain Guénoche
Alain Guénoche*
Affiliation:
IML-CNRS, 163 Av. de Luminy, 13288 Marseille Cedex 9, France; guenoche@lim.univ-mrs.fr
Get access

Abstract

We first describe four recent methods to cluster vertices of an undirected non weighted connected graph. They are all based on very different principles. The fifth is a combination of classical ideas in optimization applied to graph partitioning. We compare these methods according to their ability to recover classes initially introduced in random graphs with more edges within the classes than between them.

Keywords

Graph partitioningpartition comparisonsimulation.
Type
Research Article
Information
RAIRO - Operations Research , Volume 42 , Issue 4: ALIO/EURO V Conference on Combinatorial Optimization , October 2008 , pp. 469 - 484
Copyright
© EDP Sciences, ROADEF, SMAI, 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

C.J. Alpert and A. Kang, Recent direction in netlist partitioning: a survey, Integration. VLSI J. 19 (1-2) (1995) 1–81.
G.D. Bader and C.W. Hogue, An automated method for finding molecular complexes in large protein interaction networks. BMC Bioinformatics 4 (2) (2003) 27.
Barabasi, L., The large-scale organization of metabolic networks. Nature 407 (2000) 651–654.
V. Batagelj and M. Mrvar, Partitioning approach to visualisation of large graphs, Lect. Notes Comput. Sci. 1731, Springer (1999) 90–97.
V. Batagelj and M. Zaveršnik, An $O(m)$ algorithm for cores decomposition of networks (2001).
Brohée, S. and van Helden, J., Evaluation of clustering algorithms for protein-protein interaction networks. BMC Bioinformatics 7 (2006) 488. CrossRef
Brun, C., Herrmann, C. and Guénoche, A., Clustering proteins from interaction networks for the prediction of cellular functions. BMC Bioinformatics 5 (2004) 95. CrossRef
I. Charon, L. Denoeud, A. Guénoche, and O. Hudry, Comparing partitions by element transfert. J. Classif. 23 (1) (2006) 103–121.
T. Colombo, A. Guénoche, and Y. Quentin, Looking for high density areas in graph: Application to orthologous genes, Actes des Journées Informatiques de Metz, 2003, pp. 203–212.
The, W. Day complexity of computing metric distances between partitions. Math. Soc. Sci. 1 (1981) 269–287.
S. Van Dongen, Graph Clustering by Flow Simulation. Ph.D. Thesis, University of Utrecht (2000).
J. Duch and A. Arenas, Community detection in complex networks using Extremal Optimization, arXiv:cond-mat/0501368 (2005) 4 p.
Enright, A.J., van Dongen, S. and Ouzounis, L.A., An efficient algorithm for large-scale detection of protein families. Nucleic Acids Res. 30 (2002) 1575–1584. CrossRef
Girvan, M. and Newman, M.E.J., Community structure in social and biological networks. Proc. Natl. Acad. Sci. USA 99 (2002) 7821–7826. CrossRef
A. Guénoche, Partitions optimisées selon différents critères; Evaluation et comparaison. Math. Sci. Hum. 161 (2003) 41–58.
A. Guénoche, Clustering by vertex density in a graph, in Proceedings of IFCS congress. Classification, Clustering and Data Mining Applications, edited by D. Banks et al., Springer (2004) 15–24.
Milligan, G.W. and Cooper, M.C., An examination of procedures for determining the number of clusters in a data set. Psychometrica 50 (1985) 159–179. CrossRef
Moody, J., Identifying dense clusters in large networks. Social Networks 23 (2001) 261–283. CrossRef
M.E.J. Newman, Scientific Collaboration Networks: Shortest paths, weighted networks and centrality. Phys. Rev. (2001) 64.
Newman, M.E.J and Girvan, M., Finding and evaluating community structure in networks. Phys. Rev. E 69 (2004) 026113. CrossRef
M.E.J. Newman, Modularity and community structure in networks. arXiv:physics/0602124v1, (2006) 7 p.
P. Pons and M. Latapy, Computing communities in large networks using random walks. J. Graph Algorithms Appl. 10 (2), (2006) 191–218.
S. Régnier, Sur quelques aspects mathématiques des problèmes de classification automatique. ICC Bulletin (1964).
Rougemont, J. and Hingamp, P., DNA microarray data and contextual analysis of correlation graphs. BMC Bioinformatics 4 (2003) 15. CrossRef
Seidman, S.B., Network structure and minimum degree. Social Networks 5 (1983) 269–287. CrossRef
D. Wishart, Mode analysis: generalization of nearest neighbor which reduces chaining effects, in Numerical taxonomy, Academic Press (1976) 282–311.