Percolation phase transition of static and growing networks under a weighted function

Xiao Jia, Jin-Song Hong, Ya-Chun Gao, Hong-Chun Yang, Chun Yang, Chuan-Ji Fu and Jian-Quan Hu
Additional contact information
Xiao Jia: School of Physical Electronics, University of Electronic Science and Technology of China, Cheng Du 610054, P. R. China
Jin-Song Hong: School of Physical Electronics, University of Electronic Science and Technology of China, Cheng Du 610054, P. R. China
Ya-Chun Gao: School of Physical Electronics, University of Electronic Science and Technology of China, Cheng Du 610054, P. R. China
Hong-Chun Yang: School of Physical Electronics, University of Electronic Science and Technology of China, Cheng Du 610054, P. R. China
Chun Yang: #x2020;School of Mathematical Science, University of Electronic Science and Technology of China, Cheng Du 610054, P. R. China
Chuan-Ji Fu: School of Physical Electronics, University of Electronic Science and Technology of China, Cheng Du 610054, P. R. China
Jian-Quan Hu: School of Physical Electronics, University of Electronic Science and Technology of China, Cheng Du 610054, P. R. China

International Journal of Modern Physics C (IJMPC), 2016, vol. 27, issue 07, 1-8

Abstract: We investigate the percolation phase transitions in both the static and growing networks where the nodes are sampled according to a weighted function with a tunable parameter α. For the static network, i.e. the number of nodes is constant during the percolation process, the percolation phase transition can evolve from continuous to discontinuous as the value of α is tuned. Based on the properties of the weighted function, three typical values of α are analyzed. The model becomes the classical Erdös–Rényi (ER) network model at α=1. When α=0.5, it is shown that the percolation process generates a weakly discontinuous phase transition where the order parameter exhibits an extremely abrupt transition with a significant jump in large but finite system. For α=−1, the cluster size distribution at the lower pseudo-transition point does not obey the power-law behavior, indicating a strongly discontinuous phase transition. In the case of growing network, in which the collection of nodes is increasing, a smoother continuous phase transition emerges at α=0.5, in contrast to the weakly discontinuous phase transition of the static network. At α=−1, on the other hand, probability modulation effect shows that the nature of strongly discontinuous phase transition remains the same with the static network despite the node arrival even in the thermodynamic limit. These percolation properties of the growing networks could provide useful reference for network intervention and control in practical applications in consideration of the increasing size of most actual networks.

Keywords: Percolation; growing network; phase transition (search for similar items in EconPapers)
Date: 2016
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0129183116500820
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijmpcx:v:27:y:2016:i:07:n:s0129183116500820

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0129183116500820

Access Statistics for this article

International Journal of Modern Physics C (IJMPC) is currently edited by H. J. Herrmann

More articles in International Journal of Modern Physics C (IJMPC) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().