Continuous percolation with discontinuities

51Citations
Citations of this article
51Readers
Mendeley users who have this article in their library.

Abstract

Complex networks are a highly useful tool for modeling a vast number of different real world structures. Percolation describes the transition to extensive connectedness upon the gradual addition of links. Whether single links may explosively change macroscopic connectivity in networks where, according to certain rules, links are added competitively has been debated intensely in the past three years. In a recent article [O. Riordan and L. Warnke, Explosive Percolation is Continuous, Science 333, 322 (2011).], O. Riordan and L. Warnke conclude that (i) any rule based on picking a fixed number of random vertices gives a continuous transition, and (ii) that explosive percolation is continuous. In contrast, we show that it is equally true that certain percolation processes based on picking a fixed number of random vertices are discontinuous, and we resolve this apparent paradox. We identify and analyze a process that is continuous in the sense defined by Riordan andWarnke but still exhibits infinitely many discontinuous jumps in an arbitrary vicinity of the transition point: a Devil's staircase. We demonstrate analytically that continuity at the first connectivity transition and discontinuity of the percolation process are compatible for certain competitive percolation systems.

Author supplied keywords

Cite

CITATION STYLE

APA

Nagler, J., Tiessen, T., & Gutch, H. W. (2012). Continuous percolation with discontinuities. Physical Review X, 2(3). https://doi.org/10.1103/PhysRevX.2.031009

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free