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Multilayer Networks: Metrics and Spectral Properties

  • Emanuele CozzoEmail author
  • Guilherme Ferraz de Arruda
  • Francisco A. Rodrigues
  • Yamir Moreno
Chapter
Part of the Understanding Complex Systems book series (UCS)

Abstract

Multilayer networks represent systems in which there are several topological levels each one representing one kind of interaction or interdependency between the systems’ elements. These networks have attracted a lot of attention recently because their study allows considering different dynamical modes concurrently. Here, we revise the main concepts and tools developed up to date. Specifically, we focus on several metrics for multilayer network characterization as well as on the spectral properties of the system, which ultimately enable for the dynamical characterization of several critical phenomena. The theoretical framework is also applied for description of real-world multilayer systems.

Keywords

Multiplex Networks Topological Level Coupling Graph Epidemic Spreading Process Online Social Networks (OSNs) 
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.

Notes

Acknowledgements

EC was supported by the FPI program of the Government of Aragon, Spain. This work has been partially supported by MINECO through Grant FIS2011-25167 to YM, Comunidad de Aragón (Spain) through FENOL to EC and YM; and by the EC FET-Proactive Project PLEXMATH (grant 317614) to YM. FAR and GAF thank Fapesp and CNPq for financial support give to this research.

References

  1. 1.
    Vespignani, A.: Complex networks: the fragility of interdependency. Nature 464(7291), 984–985 (2010)CrossRefADSGoogle Scholar
  2. 2.
    De Domenico, M., Solé-Ribalta, A., Cozzo, E., Kivela, M., Moreno, Y., Porter, M.A., Arenas, A.: Mathematical formulation of multilayer networks. Phys. Rev. X 3(4), 041022 (2013)Google Scholar
  3. 3.
    Boccaletti, S., Bianconi, G., Criado, R., del Genio, C.I., Gómez-Gardeñes, J., Romance, M., Sendiña-Nadal, I., Wang, Z., Zanin, M.: The structure and dynamics of multilayer networks. Phys. Rep. 544(1), 1–122 (2014)CrossRefADSMathSciNetGoogle Scholar
  4. 4.
    Kivela, M., Arenas, A., Barthelemy, M., Gleeson, J.P., Moreno, Y., Porter, M.A.: Multilayer networks. J. Complex Netw. 2(3), 203–271 (2014)CrossRefGoogle Scholar
  5. 5.
    Wellmann, B.: Physical place and cyberplace: the rise of networked individualism. Int. J. Urban Reg. Res. 1, 227–252 (2001)CrossRefGoogle Scholar
  6. 6.
    Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., Hwang, D.U.: Complex networks: structure and dynamics. Phys. Rep. 424(4), 175–308Google Scholar
  7. 7.
    Sánchez-García, R.J., Cozzo, E., Moreno, Y.: Dimensionality reduction and spectral properties of multilayer networks. Phys. Rev. E 89(5), 052815Google Scholar
  8. 8.
    Cozzo, E., Banos, R.A., Meloni, S., Moreno, Y.: Contact-based social contagion in multiplex networks. Phys. Rev. E 88(5), 050801Google Scholar
  9. 9.
    Radicchi, F., Arenas, A.: Abrupt transition in the structural formation of interconnected networks. Nat. Phys. 9, 717–720 (2013)CrossRefGoogle Scholar
  10. 10.
    De Domenico, M., Sole-Ribalta, A., Gomez, S., Arenas, A.: Navigability of interconnected networks under random failures. PNAS 111, 8351–8356 (2014)CrossRefADSGoogle Scholar
  11. 11.
    Cardillo, A.: Gomez-Gardenes, J., Zanin, M., Romance, M., Papo, D., del Pozo, F., Boccaletti, S.: Emergence of network features from multiplexity. Sci. Rep. 3 (2013). http://www.nature.com/articles/srep01344
  12. 12.
    Chen, B.L., Hall, D.H., Chklovskii, D.B.: Wiring optimization can relate neuronal structure and function. PNAS 103(12), 4723–4728 (2006)CrossRefADSGoogle Scholar
  13. 13.
    De Domenico, M., Porter, M.A., Arenas, A.: MuxViz: a tool for multilayer analysis and visualization of networks. J. Complex Netw. (2014). doi:10.1093/comnet/cnu038Google Scholar
  14. 14.
    Stark, C., Breitkreutz, B.-J., Reguly, T., Boucher, L., Breitkreutz, A., Tyers, M.: Biogrid: a general repository for interaction datasets. Nucleic Acids Res. 34(1), D535–D539 (2006)CrossRefGoogle Scholar
  15. 15.
    Coleman, J., Katz, E., Menzel, H.: The diffusion of an innovation among physicians. Sociometry 20, 253–270 (1957)CrossRefGoogle Scholar
  16. 16.
    Magnani, M., Micenkova, B., Rossi, L.: Combinatorial analysis of multiple networks. arXiv:1303.4986Google Scholar
  17. 17.
    Kapferer, B.: Strategy and Transaction in an African Factory: African Workers and Indian Management in a Zambian Town. Manchester University Press, Manchester (1972)Google Scholar
  18. 18.
    Krackhardt, D.: Cognitive social structures. Soc. Netw. 9, 104–134 (1987)CrossRefMathSciNetGoogle Scholar
  19. 19.
    Snijders, T.A.B., Pattison, P.E., Robins, G.L., Handcock, M.S.: New specifications for exponential random graph models. Sociol. Methodol. 36, 99–153 (2006)CrossRefGoogle Scholar
  20. 20.
    Vickers, M., Chan, S.: Representing Classroom Social Structure. Victoria Institute of Secondary Education, Melbourne (1981)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Emanuele Cozzo
    • 1
    • 2
    Email author
  • Guilherme Ferraz de Arruda
    • 3
  • Francisco A. Rodrigues
    • 3
  • Yamir Moreno
    • 1
    • 2
    • 4
  1. 1.Institute for Biocomputation and Physics of Complex Systems (BIFI)ZaragozaSpain
  2. 2.Department of Theoretical PhysicsUniversity of ZaragozaZaragozaSpain
  3. 3.Departamento de Matemática Aplicada e Estatística, Instituto de Ciências Matemáticas e de ComputaçãoUniversidade de São PauloSão CarlosBrazil
  4. 4.Complex Networks and Systems Lagrange LabInstitute for Scientific InterchangeTurinItaly

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