Shortcut Model
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 vertices with periodic boundary conditions. Each vertex is joined to its neighbors on either side, which results in a system with edges. The network is extended by taking each node in turn and, with probability, adding an edge to a new location nodes distant.
The rewiring process allows the model to interpolate between a one-dimensional regular lattice and a two-dimensional regular lattice. When the rewiring probability, we have a one-dimensional regular lattice of size . When, every node is connected to a new location and the graph is essentially a two-dimensional lattice with and nodes in each direction. For between and, we have a graph which interpolates between the one and two dimensional regular lattices. The graphs we study are parametrized by
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