Bethe lattice

A Bethe lattice (after Hans Bethe ), also called the Cayley Tree (after Arthur Cayley ) is a connected, cycle-free graph in which each node is connected to another node z (z is also called the coordination number ). The grid can be viewed as a tree, which grows from an origin node and in which all nodes are higher in shells around the source node. The origin node can be designated as the root or origin. The number of nodes in the k-th shell is given by

Sometimes the definition is also amended so that the source node has z -1 neighbors. Due to the unique topological structure of the statistical mechanics of this lattice model is often solved exactly. This is similar to the Bethe approach for such systems.

A related graph is the Cayley graph.

• Class of graphs