Abstract
The explosive percolation problem on the complete graph is investigated via extensive numerical simulations. We obtain the cluster-size distribution at the moment when the cluster size heterogeneity becomes maximum. The distribution is found to be well described by the power-law form with the decay exponent , followed by a hump. We then use the finite-size scaling method to make all the distributions at various system sizes up to collapse perfectly onto a scaling curve characterized solely by the single exponent . We also observe that the instant of that collapse converges to a well-defined percolation threshold from below as . Based on these observations, we show that the explosive percolation transition in the model should be continuous, contrary to the widely spread belief of its discontinuity.
- Received 23 March 2011
DOI:https://doi.org/10.1103/PhysRevE.84.020101
©2011 American Physical Society