Incipient spanning cluster on small-world networks

We analyze the scaling properties of the largest cluster size for the site percolation problem on small-world graphs. It is shown how the presence of the extra length-scale, the small-world crossover length xi, influences the fractal dimension D of the spanning cluster. Using the results for dimensi on d = 2 we nd the critical exponent governing the cluster size distributio n tau similar or equal to5/2. This implies that is universal and independen t of d in agreement with the conjecture by Moore and Newman.