A shuffle-exchange graph is a nonsimple graph (due to the existence of graph loops) whose vertices are length binary strings with an edge from to if

1. differs from in its last bit, or

2. is obtained from by a left or right cyclic shift.

The -dimensional
shuffle-exchange graph is implemented as `ShuffleExchangeGraph`[*n*]
in the Wolfram Language package `Combinatorica``
.

For , 2, ..., the shuffle exchange graphs with self-loops removed are isomorphic to , , , ..., where is a path graph and denotes the th -vertex graph in the ordering of McKay.