Enhancing Space-Aware Community Detection Using Degree Constrained Spatial Null Model

  • Remy CazabetEmail author
  • Pierre Borgnat
  • Pablo Jensen
Conference paper
Part of the Springer Proceedings in Complexity book series (SPCOM)


Null models have many applications on networks, from testing the significance of observations to the conception of algorithms such as community detection. They usually preserve some network properties, such as degree distribution. Recently, some null-models have been proposed for spatial networks, and applied to the community detection problem. In this article, we propose a new null-model adapted to spatial networks, that, unlike previous ones, preserves both the spatial structure and the degrees of nodes. We show the efficacy of this null-model in the community detection case on synthetic networks.


Null Model Community Detection Normalize Mutual Information Radiation Model Spatial Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work is funded in part by the ANR Vel’Innov: Vel’Innov ANR-12-SOIN-0001-02, European Commission H2020 FETPROACT 2016–2017 program under grant 732942 (ODYCCEUS), by the ANR (French National Agency of Research) under grants ANR-15-CE38-0001 (AlgoDiv) and ANR-13-CORD-0017-01 (CODDDE), by the French program “PIA - Usages, services et contenus innovants” under grant O18062-44430 (REQUEST), and by the Ile-de-France program FUI21 under grant 16010629 (iTRAC).


  1. 1.
    Denise, A., Vasconcellos, M., Welsh, D.J.: The random planar graph. Congressus Numerantium, 61–80 (1996)Google Scholar
  2. 2.
    Barthélemy, M.: Spatial networks. Phys. Rep. 499(1), 1–101 (2011)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    Expert, P., Evans, T., Blondel, V., Lambiotte, R.: Uncovering space-independent communities in spatial networks. Proc. Natl. Acad. Sci. 108(19), 7663–7668 (2011)ADSCrossRefzbMATHGoogle Scholar
  4. 4.
    Blondel, V., Guillaume, J., Lambiotte, R., Lefebvre, E.: Fast unfolding of communities in large networks. J. Stat. Mech. Theory Exp. 2008(10), P10008 (2008)CrossRefGoogle Scholar
  5. 5.
    Liu, Y., Sui, Z., Kang, C., Gao, Y.: Uncovering patterns of inter-urban trip and spatial interaction from social media check-in data. PloS One 9(1), e86026 (2014)ADSCrossRefGoogle Scholar
  6. 6.
    Austwick, M.Z., OBrien, O., Strano, E., Viana, M.: The structure of spatial networks and communities in bicycle sharing systems. PloS One 8(9), e74685 (2013)ADSCrossRefGoogle Scholar
  7. 7.
    Sarzynska, M., Leicht, E.A., Chowell, G., Porter, M.A.: Null models for community detection in spatially embedded, temporal networks. J. Complex Netw. cnv027 (2015)Google Scholar
  8. 8.
    Newman, M.E.: Modularity and community structure in networks. Proc. Natl. Acad. Sci. 103(23), 8577–8582 (2006)ADSCrossRefGoogle Scholar
  9. 9.
    Lenormand, M., Bassolas, A., Ramasco, J.J.: Systematic comparison of trip distribution laws and models. J. Transp. Geogr. 51, 158–169 (2016)CrossRefGoogle Scholar
  10. 10.
    Simini, F., González, M.C., Maritan, A., Barabási, A.-L.: A universal model for mobility and migration patterns. Nature 484(7392), 96–100 (2012)ADSCrossRefGoogle Scholar
  11. 11.
    Strehl, A., Ghosh, J.: Cluster ensembles—a knowledge reuse framework for combining multiple partitions. J. Mach. Learn. Res. 3, 583–617, Dec. 2002Google Scholar
  12. 12.
    Williams, I.: A comparison of some calibration techniques for doubly constrained models with an exponential cost function. Transp. Res. 10(2), 91–104 (1976)ADSCrossRefGoogle Scholar
  13. 13.
    Newman, M.E., Strogatz, S.H., Watts, D.J.: Random graphs with arbitrary degree distributions and their applications. Phys. Rev. E 64(2), 026118 (2001)ADSCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Sorbonne Universites, UPMC Univ Paris 06ParisFrance
  2. 2.CNRS, Laboratoire de PhysiqueUniv Lyon, Ens de Lyon, Univ Claude BernardVilleurbanneFrance

Personalised recommendations