The rewiring process allows the model to interpolate between a one-dimensional regular lattice and a two-dimensional regular lattice. When the rewiring probability p = 0 , we have a one-dimensional regular lattice of size N . When p = 1 , every node is connected to a new location and the graph is essentially a two-dimensional lattice with m and N / m nodes in each direction. For p between 0 and 1 , we have a graph which interpolates between the one and two dimensional regular lattices. The graphs we study are parametrized by