Explosive percolation with cluster aggregation model

How clusters is aggregated have great effect on the function and dynamic of complex network. A percolation transition model is introduced in this paper which can be described with the clusters aggregated probability p(C
_i
)~1-C
_i
/ (C
_max
+ α), where C
_i
is the size of the cluster, C
_max
is the size of the largest cluster and α is disturbance parameter. This model respectively introduce weakly and strongly discontinuous percolation transition underlying the different α and reveal the strongly impact of clusters' aggregated probability.