Role Detection: Network Partitioning and Optimal Model of the Lumped Markov Chain

  • Maguy Trefois
  • Jean-Charles Delvenne
Conference paper
Part of the Springer Proceedings in Complexity book series (SPCOM)


Nowadays, complex networks are present in many fields (social science, chemistry, biology, …) as they allow to model systems with interacting agents. In many cases, the number of interacting agents is large (from hundreds to millions of nodes). In order to get information about the functionality of the underlying system, we are interested in studying the structure of the network. One way to do that is by partitioning the network. In this paper, we present a method to detect a partition of the network such that the dynamics of a random walker on the lumped network is a good model of the dynamics of a random walker in the original network.



We acknowledge support from the Belgian Programme of Interuniversity Attraction Poles and an Action de Recherche Concertée (ARC) of the French Community of Belgium.


  1. 1.
    Aynaud T, Guillaume JL (2011) Multi-step community detection and hierarchical time segmentation in evolving networks. In: Proceedings of the 5th SNA-KDD workshop Google Scholar
  2. 2.
    Blondel V, Guillaume J-L, Lambiotte R, Lefèvre E (2008) Fast unfolding of communities in large networks. J Stat Mech Theory Exp. doi: 10.1088/1742-5468/2008/10/P10008 Google Scholar
  3. 3.
    Browet A, Absil PA, Van Dooren P (2011) Community detection for hierarchical image segmentation. In: Proceedings of the 14th international conference on combinatorial image analysis, IWCIA’11, pp 358–371 CrossRefGoogle Scholar
  4. 4.
    Cason T (2012) Node-to-node similarity measures and role extraction in networks. PhD thesis, Université catholique de Louvain, Belgium Google Scholar
  5. 5.
    Cooper K, Barahona M (2010) Role-based similarity in directed networks. E-print. arXiv:1012.2726
  6. 6.
    Delvenne JC, Yaliraki SN, Barahona M (2010) Stability of graph communities across time scales. Proc Natl Acad Sci USA 107:12755–12760 ADSCrossRefGoogle Scholar
  7. 7.
    E W, Li T, Vanden-Eijnden E (2008) Optimal partition and effective dynamics of complex networks. Proc Natl Acad Sci USA 105:7907–7912 MathSciNetADSzbMATHCrossRefGoogle Scholar
  8. 8.
    Fortunato S (2010) Community detection in graphs. Phys Rep 486:75–174 MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    Lambiotte R, Delvenne J-C, Barahona M (2009) Laplacian dynamics and multiscale modular structure in networks. arXiv:0812.1770
  10. 10.
    Mucha P et al. (2010) Community structure in time-dependent, multiscale, and multiplex networks. Science 328:876 MathSciNetADSzbMATHCrossRefGoogle Scholar
  11. 11.
    Reichardt J, White DR (2007) Role models for complex networks. Eur Phys J B 60:217–224 ADSzbMATHCrossRefGoogle Scholar
  12. 12.
    Schaub M, Delvenne J-C, Yaliraki SN, Barahona M (2012) Markov dynamics as a zooming lens for multiscale community detection: non clique-like communities and the field-of-view limit. PLoS ONE 7:e32210 ADSCrossRefGoogle Scholar
  13. 13.
    Traag VA, Van Dooren P, Nesterov Y (2011) Narrow scope for resolution-limit-free community detection. Phys Rev E 84:016114 ADSCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Maguy Trefois
    • 1
  • Jean-Charles Delvenne
    • 1
    • 2
    • 3
  1. 1.Department of Applied MathematicsUniversité catholique de LouvainLouvain-la-NeuveBelgium
  2. 2.Facultés Universitaires Notre-Dame de la PaixNamur Complex Systems Center (NAXYS)NamurBelgium
  3. 3.Center for Operations Research and Econometrics (CORE)Université catholique de LouvainLouvain-la-NeuveBelgium

Personalised recommendations