publication . Preprint . Article . 2016

Random walk in degree space and the time-dependent Watts-Strogatz model

H. L. Casa Grande; M. Cotacallapa; M. O. Hase;
Open Access English
  • Published: 14 Oct 2016
In this work, we propose a scheme that provides an analytical estimate for the time-dependent degree distribution of some networks. This scheme maps the problem into a random walk in degree space, and then we choose the paths that are responsible for the dominant contributions. The method is illustrated on the dynamical versions of the Erd\"os-R\'enyi and Watts-Strogatz graphs, which were introduced as static models in the original formulation. We have succeeded in obtaining an analytical form for the dynamics Watts-Strogatz model, which is asymptotically exact for some regimes.
Persistent Identifiers
arXiv: Computer Science::Social and Information NetworksPhysics::Physics and Society
free text keywords: Physics - Physics and Society, Condensed Matter - Statistical Mechanics, Computer Science - Social and Information Networks, Discrete mathematics, Mathematics, In degree, Degree distribution, Graph, Random walk, Applied mathematics
19 references, page 1 of 2

[1] R. Albert and A.-L. Barabasi, Rev. Mod. Phys. 74, 47 (2002)

[2] S. N. Dorogovtsev and J. F. F. Mendes, Evolution of Networks (Oxford University Press, New York, 2003)

[3] M. E. J. Newman, SIAM Review 45, 167 (2003)

[4] S. Boccaletti, V. Latora, Y. Moreno, M. Chavez and D.- U. Hwang, Phys. Rep. 424, 175 (2006)

[5] M. E. J. Newman, A.-L. Barabasi and D. J. Watts, The Structure and Dynamics of Networks (Princeton University Press, New York, 2006)

[6] M. E. J. Newman, Networks: An Introduction (Oxford University Press, New York, 2010)

[7] M. Girvan and M. E. J. Newman, PNAS 99, 7821 (2002)

[8] M. E. J. Newman and M. Girvan, Phys. Rev. E 69, 026113 (2004)

[9] S. Boccaletti, G. Bianconi, R. Criado, C.I. del Genio, J. Gomez-Garden~es, M. Romance, I. Sendin~a-Nadal, Z. Wang and M. Zanin, Phys. Rep. 544, 1 (2014)

[10] M. Kivella, A. Arenas, M. Barthelemy, J. P. Gleeson, Y. Moreno and M. A. Porter, J. Compomplex Networks 2, 203 (2014)

[11] G. Bianconi, Eur. Phys. Lett. 81, 28005 (2008)

[12] K. Anand and G. Bianconi, Phys. Rev. E 80, 045102(R) (2009)

[13] R. Pastor-Satorras, C. Castellano, P. Van Mieghem and A. Vespignani, Rev. Mod. Phys. 87, 925 (2015)

[14] S. N. Dorogovtsev, A. V. Goltsev and J. F. F. Mendes, Rev. Mod. Phys. 80, 1275 (2008)

[15] D. Watts and S. H. Strogatz, Nature 393, 440 (1998)

19 references, page 1 of 2
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