a game played on top of a network or graph, the individuals of a population are located on the vertices of the graph. The edges of the graph determine the links through which individuals can interact. In a spatial model for the prisoner dilemma, the players are classified either as cooperators or defectors, and it is assumed that every agent can only play with his/her neighbours.

It has been shown that extremely simple rules determine whether network reciprocity can favor cooperation [@oht]. But it is the concept that cooperators can prevail by forming clusters what we want to analyze here. This idea has been discussed and analyzed in many works. In [@now1] it is found that cooperators can prevail by forming network clusters, where they help each other. In one of the pioneering works on spatially extended games [@now3] the authors have analyzed several shapes for a cluster of cooperators and test the stability of each one against the invasion by defectors. They found that cooperators can only survive and grow if they form clusters. Another work pointing out the clustering effect is [@doe] where it was stated that cooperators can survive by forming clusters within which they benefit from 