Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30174
Percolation Transition with Hidden Variables in Complex Networks

Authors: Zhanli Zhang, Wei Chen, Xin Jiang, Lili Ma, Shaoting Tang, Zhiming Zheng

Abstract:

A new class of percolation model in complex networks, in which nodes are characterized by hidden variables reflecting the properties of nodes and the occupied probability of each link is determined by the hidden variables of the end nodes, is studied in this paper. By the mean field theory, the analytical expressions for the phase of percolation transition is deduced. It is determined by the distribution of the hidden variables for the nodes and the occupied probability between pairs of them. Moreover, the analytical expressions obtained are checked by means of numerical simulations on a particular model. Besides, the general model can be applied to describe and control practical diffusion models, such as disease diffusion model, scientists cooperation networks, and so on.

Keywords: complex networks, percolation transition, hidden variable, occupied probability.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1329899

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1165

References:


[1] R. Albert and A. L. Barab'asi, Rev. Mod. Phys. 74, 47 (2002).
[2] S. Yoon, S. H. Yook, and Y. Kim, Phys. Rev. E 76, 056104 (2007).
[3] D. J. Watts, and S. H. Strogatz, Nature (London) 393, 440 (1998).
[4] A. L. Barab'asi, and R. Albert, Science 286, 509(1999)
[5] M. E. J. Newman, S. H. Strogatz, and D. J. Watts, Phys. Rev. E 64, 026118 (2001).
[6] S. N. Dorogovtsev, and J. F. F. Mendes, Adv. Phys. 51, 1079 (2002).
[7] D. S. Callaway, M. E. J. Newman, S. H. Strogatz, and D. J. Watts, Phys. Rev. Lett. 85, 5468 (2000).
[8] A. V. Goltsev, S. N. Dorogovtsev, and J. F. F. Mendes, Phys. Rev. E 78, 051105 (2008).
[9] M. A' . Serrano and P. D. L. Rios, Phys. Rev. E 76, 056121 (2007).
[10] A. Zen, A. Kabakc┬©─▒o╦çglu, and A. L. Stella, Phys. Rev. E 76, 016110 (2007).
[11] E. L'oez, R. Parshani, R. Cohen, S. Carmi, and S. Havlin, Phys. Rev. Lett. 99, 188701 (2007).
[12] J. D. Noh, Phys. Rev. E 76, 026116 (2007).
[13] M. E. J. Newman and R. M. Ziff, Phys. Rev. E 64, 016706 (2001).
[14] R. P. Satorras and A. Vespignani, Phys. Rev. Lett. 86, 3200 (2001).
[15] C. Moore and M. E. J. Newman, Phys. Rev. E 61, 5678 (2000).
[16] M. Bogu˜n'a and R. P. Satorras, Phys. Rev. E 66, 047104 (2002).
[17] J. D. Noh, Phys. Rev. E 76, 026116 (2007).
[18] A. V. Goltsev, S. N. Dorogovtsev, and J. F. F. Mendes, Phys. Rev. E 78, 051105 (2008).
[19] A. Zen, A. Kabakcıoˇglu, and A. L. Stella, Phys. Rev. E 76, 026110 (2007).
[20] M. A. Serrano and P. D. L. Rios, Phys. Rev. E 76, 056121(2007).
[21] E. L'opez, R. Parshani, R. Cohen, S. Carmi, and S. Havlin, Phys. Rev. E 99, 188701 (2007).
[22] L. Apolo, O. Melchert, and A. K. Hartmann, Phys. Rev. E 79, 031103 (2009).
[23] D. Stauffer and A. Aharony, Introduction to Percolation Theory, 2nd edition, Taylor and Francis, London (1992).
[24] G. Caldarelli, A. Capocci, P. D. L. Rios, and M. A. Mun˜noz5, Phys. Rev. Lett. 89, 258702 (2002).
[25] B. S¨oderberg, Phys. Rev. E 66, 066126 (2002).
[26] M. Bogu˜n'a and R. P. Satorras, Phys. Rev. E 68, 036112 (2003).