Comparison of algorithms in graph partitioning
RAIRO - Operations Research - Recherche Opérationnelle, Tome 42 (2008) no. 4, pp. 469-484.

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.

DOI : 10.1051/ro:2008029
Classification : 05C85, 90C35, 90C59
Mots-clés : graph partitioning, partition comparison, simulation
@article{RO_2008__42_4_469_0,
     author = {Gu\'enoche, Alain},
     title = {Comparison of algorithms in graph partitioning},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {469--484},
     publisher = {EDP-Sciences},
     volume = {42},
     number = {4},
     year = {2008},
     doi = {10.1051/ro:2008029},
     mrnumber = {2469107},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/ro:2008029/}
}
TY  - JOUR
AU  - Guénoche, Alain
TI  - Comparison of algorithms in graph partitioning
JO  - RAIRO - Operations Research - Recherche Opérationnelle
PY  - 2008
SP  - 469
EP  - 484
VL  - 42
IS  - 4
PB  - EDP-Sciences
UR  - http://archive.numdam.org/articles/10.1051/ro:2008029/
DO  - 10.1051/ro:2008029
LA  - en
ID  - RO_2008__42_4_469_0
ER  - 
%0 Journal Article
%A Guénoche, Alain
%T Comparison of algorithms in graph partitioning
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 2008
%P 469-484
%V 42
%N 4
%I EDP-Sciences
%U http://archive.numdam.org/articles/10.1051/ro:2008029/
%R 10.1051/ro:2008029
%G en
%F RO_2008__42_4_469_0
Guénoche, Alain. Comparison of algorithms in graph partitioning. RAIRO - Operations Research - Recherche Opérationnelle, Tome 42 (2008) no. 4, pp. 469-484. doi : 10.1051/ro:2008029. http://archive.numdam.org/articles/10.1051/ro:2008029/

[1] C.J. Alpert and A. Kang, Recent direction in netlist partitioning: a survey, Integration. VLSI J. 19 (1-2) (1995) 1-81. | Zbl

[2] 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.

[3] L. Barabasi, The large-scale organization of metabolic networks. Nature 407 (2000) 651-654.

[4] V. Batagelj and M. Mrvar, Partitioning approach to visualisation of large graphs, Lect. Notes Comput. Sci. 1731, Springer (1999) 90-97. | MR

[5] V. Batagelj and M. Zaveršnik, An O(m) algorithm for cores decomposition of networks (2001).

[6] S. Brohée and J. Van Helden, Evaluation of clustering algorithms for protein-protein interaction networks. BMC Bioinformatics 7 (2006) 488.

[7] C. Brun, C. Herrmann and A. Guénoche, Clustering proteins from interaction networks for the prediction of cellular functions. BMC Bioinformatics 5 (2004) 95.

[8] I. Charon, L. Denoeud, A. Guénoche, and O. Hudry, Comparing partitions by element transfert. J. Classif. 23 (1) (2006) 103-121. | MR

[9] 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.

[10] W. Day, The complexity of computing metric distances between partitions. Math. Soc. Sci. 1 (1981) 269-287. | MR | Zbl

[11] S. Van Dongen, Graph Clustering by Flow Simulation. Ph.D. Thesis, University of Utrecht (2000).

[12] J. Duch and A. Arenas, Community detection in complex networks using Extremal Optimization, arXiv:cond-mat/0501368 (2005) 4 p.

[13] A.J. Enright, S. Van Dongen and L.A. Ouzounis, An efficient algorithm for large-scale detection of protein families. Nucleic Acids Res. 30 (2002) 1575-1584.

[14] M. Girvan and M.E.J. Newman, Community structure in social and biological networks. Proc. Natl. Acad. Sci. USA 99 (2002) 7821-7826. | MR | Zbl

[15] A. Guénoche, Partitions optimisées selon différents critères; Evaluation et comparaison. Math. Sci. Hum. 161 (2003) 41-58. | MR

[16] 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. | MR

[17] G.W. Milligan and M.C. Cooper, An examination of procedures for determining the number of clusters in a data set. Psychometrica 50 (1985) 159-179.

[18] J. Moody, Identifying dense clusters in large networks. Social Networks 23 (2001) 261-283.

[19] M.E.J. Newman, Scientific Collaboration Networks: Shortest paths, weighted networks and centrality. Phys. Rev. (2001) 64.

[20] M.E.J Newman and M. Girvan, Finding and evaluating community structure in networks. Phys. Rev. E 69 (2004) 026113.

[21] M.E.J. Newman, Modularity and community structure in networks. arXiv:physics/0602124v1, (2006) 7 p. | MR

[22] P. Pons and M. Latapy, Computing communities in large networks using random walks. J. Graph Algorithms Appl. 10 (2), (2006) 191-218. | MR

[23] S. Régnier, Sur quelques aspects mathématiques des problèmes de classification automatique. ICC Bulletin (1964).

[24] J. Rougemont and P. Hingamp, DNA microarray data and contextual analysis of correlation graphs. BMC Bioinformatics 4 (2003) 15.

[25] S.B. Seidman, Network structure and minimum degree. Social Networks 5 (1983) 269-287. | MR

[26] D. Wishart, Mode analysis: generalization of nearest neighbor which reduces chaining effects, in Numerical taxonomy, Academic Press (1976) 282-311.

Cité par Sources :