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Constrained Community Detection in Multiplex Networks

Part of the Lecture Notes in Computer Science book series (LNISA,volume 10539)


Constrained community detection is a kind of community detection taking given constraints into account to improve the accuracy of community detection. Optimizing constrained Hamiltonian is one of the methods for constrained community detection. Constrained Hamiltonian consists of Hamiltonian which is generalized modularity and constrained term which takes given constraints into account. Nakata proposed a method for constrained community detection in monoplex networks based on the optimization of constrained Hamiltonian by extended Louvain method.

In this paper, we propose a new method for constrained community detection in multiplex networks. Multiplex networks are the combinations of multiple individual networks. They can represent temporal networks or networks with several types of edges. While optimizing modularity proposed by Mucha et al. is popular for community detection in multiplex networks, our method optimizes the constrained Hamiltonian which we extend for multiplex networks. By using our proposed method, we successfully detect communities taking constraints into account. We also successfully improve the accuracy of community detection by using our method iteratively. Our method enables us to carry out constrained community detection interactively in multiplex networks.


  • Multiplex networks
  • Constrained community detection
  • Gen Louvain method
  • Constrained Hamiltonian

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  1. Blondel, V.D., Guillaume, J.L., Lambiotte, R., Lefebvre, E.: Fast unfolding of communities in large networks. J. Stat. Mech.: Theory Exp. 2008(10), P10008 (2008). doi:10.1088/1742-5468/2008/10/P10008

    CrossRef  Google Scholar 

  2. De Domenico, M., Lancichinetti, A., Arenas, A., Rosvall, M.: Identifying modular flows on multilayer networks reveals highly overlapping organization in social systems. Phys. Rev. X 5, 011027 (2015). doi:10.1103/PhysRevX.5.011027

    Google Scholar 

  3. De Domenico, M., Porter, M.A., Arenas, A.: MuxViz: a tool for multilayer analysis and visualization of networks. J. Complex Netw. 3(2), 159–176 (2015). doi:10.1093/comnet/cnu038

    CrossRef  Google Scholar 

  4. Eaton, E., Mansbach, R.: A spin-glass model for semi-supervised community detection. In: Proceedings of the Twenty-Sixth AAAI Conference on Artificial Intelligence (AAAI-2012), pp. 900–906 (2012)

    Google Scholar 

  5. Jutla, I.S., Jeub, L.G.S., Mucha, P.J.: A generalized Louvain method for community detection implemented in matlab (2011–2014).

  6. Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983). doi:10.1126/science.220.4598.671

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. Kivelä, M., Arenas, A., Barthelemy, M., Gleeson, J.P., Moreno, Y., Porter, M.A.: Multilayer networks. J. Complex Netw. 2(3), 203–271 (2014). doi:10.1093/comnet/cnu016

    CrossRef  Google Scholar 

  8. Mucha, P.J., Richardson, T., Macon, K., Porter, M.A., Onnela, J.P.: Community structure in time-dependent, multiscale, and multiplex networks. Science 328(5980), 876–878 (2010). doi:10.1126/science.1184819

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. Nakata, K., Murata, T.: Fast optimization of hamiltonian for constrained community detection. In: Mangioni, G., Simini, F., Uzzo, S.M., Wang, D. (eds.) Complex Networks VI. SCI, vol. 597, pp. 79–89. Springer, Cham (2015). doi:10.1007/978-3-319-16112-9_8

    Google Scholar 

  10. Newman, M.E.J., Girvan, M.: Finding and evaluating community structure in networks. Phys. Rev. E 69, 026113 (2004). doi:10.1103/PhysRevE.69.026113

    CrossRef  Google Scholar 

  11. Padgett, J.F., Ansell, C.K.: Robust action and the rise of the medici, 1400–1434. Am. J. Sociol. 98(6), 1259–1319 (1993). doi:10.1086/230190

    CrossRef  Google Scholar 

  12. Reichardt, J., Bornholdt, S.: Statistical mechanics of community detection. Phys. Rev. E 74, 016110 (2006). doi:10.1103/PhysRevE.74.016110

    CrossRef  MathSciNet  Google Scholar 

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This work was supported by Tokyo Tech - Fuji Xerox Cooperative Research (Project Code KY260195), JSPS Grant-in-Aid for Scientific Research(B) (Grant Number 17H01785) and JST CREST (Grant Number JPMJCR1687).

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Correspondence to Tsuyoshi Murata .

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Eguchi, K., Murata, T. (2017). Constrained Community Detection in Multiplex Networks. In: Ciampaglia, G., Mashhadi, A., Yasseri, T. (eds) Social Informatics. SocInfo 2017. Lecture Notes in Computer Science(), vol 10539. Springer, Cham.

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