Percolation Transitions in Scale-Free Networks under the Achlioptas Process
- 23 September 2009
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 103 (13), 135702
- https://doi.org/10.1103/physrevlett.103.135702
Abstract
It has been recently shown that the percolation transition is discontinuous in Erdős-Rényi networks and square lattices in two dimensions under the Achlioptas process (AP). Here, we show that when the structure is highly heterogeneous as in scale-free networks, a discontinuous transition does not always occur: a continuous transition is also possible depending on the degree distribution of the scale-free network. This originates from the competition between the AP that discourages the formation of a giant component and the existence of hubs that encourages it. We also estimate the value of the characteristic degree exponent that separates the two transition types.Other Versions
This publication has 8 references indexed in Scilit:
- Explosive Growth in Biased Dynamic Percolation on Two-Dimensional Regular Lattice NetworksPhysical Review Letters, 2009
- Explosive Percolation in Random NetworksScience, 2009
- Dynamics of jamming transitions in complex networksEurophysics Letters, 2005
- Evolution of scale-free random graphs: Potts model formulationNuclear Physics B, 2004
- Connected Components in Random Graphs with Given Expected Degree SequencesAnnals of Combinatorics, 2002
- Universal Behavior of Load Distribution in Scale-Free NetworksPhysical Review Letters, 2001
- First-order transition in small-world networksEurophysics Letters, 2000
- Scaling for first-order phase transitions in thermodynamic and finite systemsPhysical Review B, 1982