The shortcut model starts with a network built on a one-dimensional regular lattice. One then adds edges to create shortcuts that join remote parts of the lattice to one another. The starting network is a one-dimensional lattice of N vertices with periodic boundary conditions. Each vertex is joined to its neighbors on either side, which results in a system with N edges. The network is extended by taking each node in turn and, with probability p , adding an edge to a new location m nodes distant.