has a first vertex but no last vertex.
* A directed trail is a directed walk in which all edges are distinct.
* A directed path is a directed trail in which all vertices are distinct.

If is a finite directed walk with vertex sequence then is said to be a walk from to . Similarly for a directed trail or a path. If there is a finite directed walk between two distinct vertices then there is also a finite directed trail and a finite directed path between them.

A "simple directed path" is a path where all

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