- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Localization of multilayer networks by optimized single-layer rewiring

Sarika Jalan1,2,* and Priodyuti Pradhan1

  • 1Complex Systems Lab, Discipline of Physics, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore 453552, India
  • 2Centre for Biosciences and Biomedical Engineering, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore 453552, India

  • *sarikajalan9@gmail.com
PDF

Phys. Rev. E 97, 042314 – Published 23 April, 2018

DOI: https://doi.org/10.1103/PhysRevE.97.042314

Abstract

We study localization properties of principal eigenvectors (PEVs) of multilayer networks (MNs). Starting with a multilayer network corresponding to a delocalized PEV, we rewire the network edges using an optimization technique such that the PEV of the rewired multilayer network becomes more localized. The framework allows us to scrutinize structural and spectral properties of the networks at various localization points during the rewiring process. We show that rewiring only one layer is enough to attain a MN having a highly localized PEV. Our investigation reveals that a single edge rewiring of the optimized MN can lead to the complete delocalization of a highly localized PEV. This sensitivity in the localization behavior of PEVs is accompanied with the second largest eigenvalue lying very close to the largest one. This observation opens an avenue to gain a deeper insight into the origin of PEV localization of networks. Furthermore, analysis of multilayer networks constructed using real-world social and biological data shows that the localization properties of these real-world multilayer networks are in good agreement with the simulation results for the model multilayer network. This paper is relevant to applications that require understanding propagation of perturbation in multilayer networks.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (43)

  1. M. D. Domenico, C. Granell, M. A. Porter, and A. Arenas, Nat. Phys. 12, 901 (2016).
  2. S. Boccaletti, G. Bianconi, R. Criado, C. I. del Genio, J. Gómez-Gardeñes, M. Romance, I. Sendiña-Nadal, Z. Wang, and M. Zanin, Phys. Rep. 544, 1 (2014).
  3. C. Sarkar, A. Yadav, and S. Jalan, Europhys. Lett. 113, 18007 (2016).
  4. S. Jalan and A. Singh, Europhys. Lett. 113, 30002 (2016).
  5. S. K. Dwivedi, C. Sarkar, and S. Jalan, Europhys. Lett. 111, 10005 (2015).
  6. S. K. Dwivedi, M. S. Baptista, and S. Jalan, Phys. Rev. E 95, 040301 (2017).
  7. P. Shinde and S. Jalan, Europhys. Lett. 112, 58001 (2015).
  8. S. Osat, A. Faqeeh, and F. Radicchi, Nat. Commun. 8, 1540 (2017).
  9. S. Timóteo, M. Correia, S. R. Echeberría, H. Freitas, and R. Heleno, Nat. Commun. 9, 140 (2018).
  10. C. I. del Genio, J. Gómez-Gardeñes, I. Bonamassa, and S. Boccaletti, Sci. Adv 2, e1601679 (2016).
  11. D. S. Bassett and O. Sporns, Nat. Neurosci. 20, 3 (2017).
  12. M. S. Baptista, F. M. Moukam Kakmeni, and C. Grebogi, Phys. Rev. E 82, 036203 (2010).
  13. S. Jalan, S. Ghosh, and B. Patra, Chaos 27, 101104 (2017).
  14. K. K. Kleinberg, M. Boguna, M. A. Serrano, and F. Papadopoulos, Nat. Phys. 12, 1076 (2016).
  15. D. S. Bassett, N. F. Wymbs, M. A. Porter, P. J. Mucha, J. M. Carlson, and S. T. Grafton, Proc. Natl. Acad. Sci. USA 108, 7641 (2011).
  16. B. L. Chen, D. H. Hall, and D. B. Chklovskil, Proc. Natl. Acad. Sci. USA 103, 4723 (2006).
  17. S. H. Strogatz, Nature (London) 410, 268 (2001).
  18. A. V. Goltsev, S. N. Dorogovtsev, J. G. Oliveira, and J. F. F. Mendes, Phys. Rev. Lett. 109, 128702 (2012).
  19. P. V. Mieghem, Europhys. Lett. 97, 48004 (2012).
  20. J. Aguirre, D. Papo, and J. M. Buldú, Nat. Phys. 9, 230 (2013).
  21. C. Castellano and R. Pastor-Satorras, Phys. Rev. X 7, 041024 (2017).
  22. P. Pradhan, A. Yadav, S. K. Dwivedi, and S. Jalan, Phys. Rev. E 96, 022312 (2017).
  23. R. Chaudhuri, A. Bernacchia, and X. J. Wang, eLife 3, e01239 (2014).
  24. R. Pastor-Satorras and C. Castellano, Sci. Rep. 6, 18847 (2016).
  25. F. Slanina, Phys. Rev. E 95, 052149 (2017).
  26. P. Moretti and M. A. Muñoz, Nat. Commun. 4, 2521 (2013).
  27. G. F. de Arruda, E. Cozzo, T. P. Peixoto, F. A. Rodrigues, and Y. Moreno, Phys. Rev. X 7, 011014 (2017).
  28. P. V. Mieghem, Graph Spectra for Complex Networks (Cambridge University Press, Cambridge, England, 2011).
  29. T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to Algorithms, 3rd ed. (MIT Press, Cambridge, MA, 2009).
  30. S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Science 220, 4598 (1983).
  31. A.-L. Barabási, Network Science (Cambridge University Press, Cambridge, England, 2016).
  32. L. V. Tran, V. H. Vu, and K. Wang, Random Struct. Algorithms 42, 110 (2013).
  33. S. Jalan and S. K. Dwivedi, Phys. Rev. E 89, 062718 (2014).
  34. E. Omodei, M. D. Domenico, and A. Arenas, Front. Phys. 3, 59 (2015).
  35. C. Stark, B. J. Breitkreutz, T. Reguly, L. Boucher, A. Breitkreutz, and M. Tyers, Nucl. Acids Res. 34, D535 (2006).
  36. M. D. Domenico, V. Nicosia, A. Arenas, and V. Latora, Nat. Commun. 6, 6864 (2015).
  37. M. D. Domenico, M. A. Porter, and A. Arenas, J. Complex Netw. 3, 159 (2015).
  38. A. Clauset, C. R. Shalizi, and M. E. J. Newman, SIAM Rev. 51, 661 (2009).
  39. F. Pedregosa et al., J. Mach. Learn. Res. 12, 2825 (2011).
  40. S. Jalan, N. Solymosi, G. Vattay, and B. Li, Phys. Rev. E 81, 046118 (2010).
  41. J. Coleman, E. Katz, and H. Menzel, Sociometry 20, 253 (1957).
  42. L. Peel, in Proceedings of the 2017 SIAM International Conference on Data Mining (SIAM, Texas, 2017), p. 435.
  43. P. Mahadevan, D. Krioukov, K. Fall, and A. Vahdat, in Proceedings of the 2006 Conference on Applications, Technologies, Architectures, and Protocols for Computer Communications (ACM Press, Italy, 2006), p. 135.

Outline

Information

Phys. Rev. E 97, 042314– Published 23 April, 2018
  • Received 30 November 2017
Crossmark - Check for updates button

©2018 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation