Representation Learning on a Random Lattice

In particular, we approximate percolation on a high-dimensional lattice using the Bethe lattice, a special system that corresponds to an infinite-dimensional lattice and admits exact solutions. For more details, the reader is referred to Stauffer and Aharony (1994), Bunde and Havlin (2012), and references therein. The Bethe lattice is an infinite connected undirected graph with no cycles (a tree) in which all nodes have equal degree z . The lattice centers on an arbitrary origin site, which connects to z neighbor sites. Each neighbor further connects to z 1 new sites, with each of those sites in turn connecting to z 1 new sites, such that the branching continues indefinitely 6 .