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Open Physics

formerly Central European Journal of Physics

Editor-in-Chief: Seidel, Sally

Managing Editor: Lesna-Szreter, Paulina

IMPACT FACTOR 2018: 1.005

CiteScore 2018: 1.01

SCImago Journal Rank (SJR) 2018: 0.237
Source Normalized Impact per Paper (SNIP) 2018: 0.541

ICV 2017: 162.45

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Volume 13, Issue 1


Volume 13 (2015)

Percolation on the institute-enterprise R&D collaboration networks

Chenguang Li
  • Corresponding author
  • School of Economics and Management, North China University of Technology, 100144 Beijing, P. R. China
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/ Yongan Zhang
Published Online: 2014-10-09 | DOI: https://doi.org/10.1515/phys-2015-0008


Realistic network-like systems are usually composed of multiple networks with interacting relations such as school-enterprise research and development (R&D) collaboration networks. Here, we study the percolation properties of a special class of R&D collaboration network, namely institute-enterprise R&D collaboration networks (IERDCNs). We introduce two actual IERDCNs to show their structural properties, and we present a mathematical framework based on generating functions for analyzing an interacting network with any connection probability. Then,we illustrate the percolation threshold and structural parameter arithmetic in the sub-critical and supercritical regimes.We compare the predictions of our mathematical framework and arithmetic to data for two real R&D collaboration networks and a number of simulations. We find that our predictions are in remarkable agreement with the data. We show applications of the framework to electronics R&D collaboration networks

Keywords : networks; percolation; generating function

PACS : 64.60.aq; 64.60.ah; 64.60.-i; 89.75.Fb


  • [1] R. Albert, H. Jeong, A. L. Barabasi, Nature 401, 130 (1999)Google Scholar

  • [2] D. S. Callaway, M. E. J. Newman, S. H. Strogatz, D. J.Watts, Phys. Rev. Lett. 85, 5468 (2000)Google Scholar

  • [3] M. E. J. Newman, Proc. Natl. Acad. Sci. 98, 404 (2001)Google Scholar

  • [4] J. Stelling, S. Klamt, K. Bettenbrock, S. Schuster, E. D. Gilles, Nature 420, 190 (2002)Google Scholar

  • [5] C. M. Song, S. Havlin, H. A. Makse, Nature 433, 392 (2005)Google Scholar

  • [6] J. Nagler, A. Levina, M. Timme, Nat. Phys. 7, 265 (2011)Google Scholar

  • [7] Y. Y. Liu, E. Csoka, H. J. Zhou, M. Posfai, Phys. Rev. Lett. 109, 205703 (2012)Google Scholar

  • [8] E. A. Leicht, R. M. D’Souza, arXiv:0907.0894 [cond-mat.dis-nn]Google Scholar

  • [9] S. V. Buldyrev, R. Parshani, G. Paul, H. E. Stanley, S. Havlin, Nature 464, 1025 (2010)Google Scholar

  • [10] R. Parshani, S. V. Buldyrev, S. Havlin, Phys. Rev. Lett. 105, 048701 (2010)Google Scholar

  • [11] S. V. Buldyrev, N.W. Shere, G. A. Cwilich, Phys. Rev. E 83, 016112 (2011)Google Scholar

  • [12] J. Shao, S. V. Buldyrev, S. Havlin, H. E. Stanley, Phys. Rev. E 83, 036116 (2011) Google Scholar

  • [13] J. X. Gao, S. V. Buldyrev, H. E. Stanley, S. Havlin, Nat. Phys. 8, 40 (2012)Google Scholar

  • [14] A. Bashan, R. Parshani, S. Havlin, Phys. Rev. E. 83, 051127 (2011)Google Scholar

  • [15] X. Q. Huang, J. X. Gao, S. V. Buldyrev, S. Havlin, H. E. Stanley, Phys. Rev. E 83, 065101 (2011)Google Scholar

  • [16] T. Fu, Y. N. Chen, Z. Qin, L. P. Guo, Physica A 392, 2807 (2013)Google Scholar

  • [17] S. Valverde, R. V. Sole, M. A. Bedau, N. Packard, Phys. Rev. E 76, 056118 (2007)Google Scholar

  • [18] M. E. J. Newman, S. H. Strogatz, D. J. Watts, Phys. Rev. E 64, 026118 (2001)Google Scholar

  • [19] M. E. J. Newman, Phys. Rev. E 66, 016128 (2002)Google Scholar

  • [20] T. Kalisky, R. Cohen, Phys. Rev. E 73, 035101 (2006)Google Scholar

  • [21] J. X. Gao, S. V. Buldyrev, S. Havlin, H. E. Stanley, Phys. Rev. Lett. 107, 195701 (2011) CrossrefGoogle Scholar

About the article

Received: 2013-11-21

Accepted: 2014-08-23

Published Online: 2014-10-09

Published in Print: 2015-01-01

Citation Information: Open Physics, Volume 13, Issue 1, ISSN (Online) 2391-5471, DOI: https://doi.org/10.1515/phys-2015-0008.

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© 2015 C. Li, Y. Zhang. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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