Types of Paths

Topics: Path - Graph Theory

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There are several types of paths:

• An open path is a path that ends on a vertex different from the one that it starts on. A closed path is the opposite: it starts and ends on the same vertex.

Example

For example, given the graph:

We can have the following path from $V1$ to $V6$:

$$V1,E3,V3,E10,V2,E2,V4,E11,V4,E7,V6$$

• A simple trajectory is an open path with no repeated vertices or edges.

• A circuit is a closed path with no repeated edges and just one repeated vertex (the start/end vertex).

• A directed path is a path that respects the direction of the arcs it goes through.