Condition Of Weak Discontinuity For Percolation Models With Edge Selection Rule Depending On Cluster Sizes

With regard to rapid transition in percolation on graphs, a sufficient condition for cluster sizes to realize the weak discontinuity is derived. We focused on a group of models in which edges are added between nodes with a probability depending on their cluster sizes. It is found that the Erdos-Renyi model becomes weakly discontinuous depending on some initial condition.