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
Read more about this topic: Shortcut Model
Famous quotes containing the word model:
“The best way to teach a child restraint and generosity is to be a model of those qualities yourself. If your child sees that you want a particular item but refrain from buying it, either because it isn’t practical or because you can’t afford it, he will begin to understand restraint. Likewise, if you donate books or clothing to charity, take him with you to distribute the items to teach him about generosity.”
—Lawrence Balter (20th century)