# Degeneracy graph

### From Glossary

An undirected graph, where the nodes represent bases and edges their adjacency. The degeneracy graph is a way to probe deeply into a degenerate extreme point (represented by more than one basic feasible solution). Among other things, it reveals good pivot steps through the point enroute to an optimum, and it provides a clear, efficient approach to sensitivity analysis.

- Here are some terms for a degeneracy graph associated with a (basic) solution, :
*degeneracy power*of : number of bases corresponding to .*internal node*: a node whose neighbors are all in this degeneracy graph.*transition column*: a tableau column such that a pivot exists for which that column enters the basis, and the new basis corresponds to a transition node.*transition node*: a node with at least one member outside this degeneracy graph (so a pivot moves to a different solution).*Transition Node Pivoting*(TNP)*rule*: a lexicographic rule using a special column to avoid internal nodes (but cycling is possible).