A directed edge can be reversed to generate the edge in the opposite direction.

That is, it is an orientation of a complete graph, or equivalently a directed graph in which every pair of vertices is connected by a single directed edge.

Now let be maximal such that for every there is a directed edge from to .

Intuitively, this means that the corresponding graph has a directed edge from to .

A directed edge refers to the link from the parent to the child (the arrows in the picture of the tree).

The algorithm can also be applied to an undirected graph by replacing each undirected edge with two directed edge of opposite directions.

It is defined here for undirected graphs; for directed graphs the definition of path requires that consecutive vertices be connected by an appropriate directed edge.

Using directed edges it is also possible to model one-way streets.

We can represent this directed edge by .

An augmented conflict graph is a conflict graph with added edges: In addition to the original edges a directed edge exists from transaction to transaction if two conditions are met: