Abstract
A giant cluster emerges discontinuously in bond percolation in various networks when the growth of large clusters is globally suppressed. It was recently revealed that this phenomenon occurs even in a scale-free (SF) network, where hubs accelerate the growth of large clusters. The SF network used in the previous study was disassortative, though, so it is necessary to check whether the phenomenon also occurs in an assortative SF network, where each hub prefers to be connected to another hub and thus the large cluster growth is accelerated. In this paper, we find that the phenomenon, namely the discontinuous emergence of a giant cluster in bond percolation with the global suppression of large clusters, also occurs in an assortative SF network. Interestingly, the network generated by occupied bonds has a different structure from the underlying network unlike the previous study. Specifically, the generated network is also assortative but not an SF network at the transition point, unlike the disassortative SF network generated at the transition point in the previous study. We observe similar behaviors in two additional models and discuss the results.
Similar content being viewed by others
References
D. Lee, B. Kahng, Y.S. Cho, K.-I. Goh, D.-S. Lee, J. Korean Phys. Soc. 73, 152 (2018)
D. Lee, Y.S. Cho, B. Kahng, Eur. Phys. J. Spec. Top. 124002 (2016)
N. Araújo, P. Grassberger, B. Kahng, K.J. Schrenk, R.M. Ziff, Eur. Phys. J. Spec. Top. 223, 2307 (2014)
R.M. D’Souza, J. Nagler, Nat. Phys. 11, 531 (2015)
D. Achlioptas, R.M. D’Souza, J. Spencer, Science 323, 1453 (2009)
Y.S. Cho, B. Kahng, Phys. Rev. Lett. 107, 275703 (2011)
R.M. D’Souza, M. Mitzenmacher, Phys. Rev. Lett. 104, 195702 (2010)
W. Choi, S.-H. Yook, Y. Kim, Phys. Rev. E 84, 020102 (2011)
H. Chae, S.-H. Yook, Y. Kim, Phys. Rev. E 85, 051118 (2012)
N.A.M. Araújo, H.J. Herrmann, Phys. Rev. Lett. 105, 035701 (2010)
K.J. Schrenk, A. Felder, S. Deflorin, N.A.M. Araújo, R.M. D’Souza, H.J. Herrmann, Phys. Rev. E 85, 031103 (2012)
E.J. Friedman, A.S. Landsberg, Phys. Rev. Lett. 103, 255701 (2009)
Y.S. Cho, S.-W. Kim, J.D. Noh, B. Kahng, D. Kim, Phys. Rev. E 82, 042102 (2010)
F. Radicchi, S. Fortunato, Phys. Rev. E 81, 036110 (2010)
R.M. Ziff, Phys. Rev. E 82, 051105 (2010)
R.A. da Costa, S.N. Dorogovtsev, A.V. Goltsev, J.F.F. Mendes, Phys. Rev. Lett. 105, 255701 (2010)
R.A. da Costa, S.N. Dorogovtsev, A.V. Goltsev, J.F.F. Mendes, Phys. Rev. E 90, 022145 (2014)
J. Nagler, T. Tiessen, H.W. Gutch, Phys. Rev. X 2, 031009 (2012)
P. Grassberger, C. Christensen, G. Bizhani, S.-W. Son, M. Paczuski, Phys. Rev. Lett. 106, 225701 (2011)
Y. Kang, Y.S. Cho, Phys. Rev. E 104, 014310 (2021)
J. Nagler, A. Levina, M. Timme, Nat. Phys. 7, 265 (2011)
O. Riordan, L. Warnke, Science 333, 322 (2011)
Y.S. Cho, S. Hwang, H.J. Herrmann, B. Kahng, Science 339, 1185 (2013)
S.M. Oh, S.-W. Son, B. Kahng, Phys. Rev. E 93, 032316 (2016)
S.M. Oh, S.-W. Son, B. Kahng, Phys. Rev. E 98, 060301 (2018)
K. Panagiotou, R. Spőhel, A. Steger, Notes Discrete Math. 38, 699 (2011)
Y.S. Cho, J.S. Lee, H.J. Herrmann, B. Kahng, Phys. Rev. Lett. 116, 025701 (2016)
K. Choi, W. Choi, B. Kahng, Chaos 31, 053128 (2021)
Y.S. Cho, J.S. Kim, J. Park, B. Kahng, D. Kim, Phys. Rev. Lett. 103, 135702 (2009)
F. Radicchi, S. Fortunato, Phys. Rev. Lett. 103, 168701 (2009)
K.-I. Goh, B. Kahng, D. Kim, Phys. Rev. Lett. 87, 278701 (2001)
R. Cohen, D. ben Avraham, S. Havlin, Phys. Rev. E 66, 036113 (2002)
D.S. Lee, K.-I. Goh, B. Kahng, D. Kim, Nucl. Phys. B 696, 351 (2004)
J.-S. Lee, K.-I. Goh, B. Kahng, D. Kim, Eur. Phys. J. B 49, 231 (2006)
A.V. Goltsev, S.N. Dorogovtsev, J.F.F. Mendes, Phys. Rev. E 78, 051105 (2008)
J.D. Noh, Phys. Rev. E 76, 026116 (2007)
S.-W. Kim, J.D. Noh, J. Korean Phys. Soc. 52 (2008)
Acknowledgements
This work was supported by a National Research Foundation of Korea (NRF) Grant, no. 2020R1F1A1061326.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Jeong, Y., Oh, S.M. & Cho, Y.S. Discontinuous emergence of a giant cluster in assortative scale-free networks. J. Korean Phys. Soc. 81, 608–614 (2022). https://doi.org/10.1007/s40042-022-00550-7
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40042-022-00550-7