  In this paper we characterize the superconductor-insulator phase transition
on a network of 2d percolation clusters. Sufficiently close to the percolation
threshold, this network has a broad degree distribution, and at p=p_c the
degree distribution becomes scale-free. We study the Transverse Ising Model on
this complex topology in order to characterize the superconductor-insulator
transition in a network formed by 2d percolation clusters of a superconductor
material. We show, by a mean-field treatment, that the critical temperature of
superconductivity depends on the maximal eigenvalue of the adjacency matrix of
the network. At the percolation threshold, we find that the maximal eigenvalue
of the adjacency matrix of the network of 2d percolation clusters has a
maximum. In correspondence of this maximum the superconducting critical
temperature T_c is enhanced. These results suggest the design of new
superconducting granular materials with enhanced critical temperature.
