A new route to Explosive Percolation

The biased link occupation rule in the Achlioptas process (AP) discourages the large clusters from growing much ahead of others and encourages faster growth of clusters which lag behind. In this paper we propose a model where this tendency is sharply reflected in the Gamma distribution of the cluster sizes, unlike the power law distribution in AP. In this model single edges between pairs of clusters of sizes sisi and sjsj are occupied with a probability ∝(sisj)α∝(sisj)α. The parameter αα is continuously tunable over the entire real axis. Numerical studies indicate that for α<αcα<αc the transition is first order, αc=0αc=0 for a square lattice and αc=−1/2αc=−1/2 for random graphs. In the limits of α=−∞,+∞α=−∞,+∞ this model coincides with models well established in the literature.

Research highlights
► A new route to Explosive Percolation has been defined and studied.
► This model gives a first order transition for a wide range of parameter values.
► The limiting cases of this model coincide with many well known models existing in the literature.