Directed cycle

Definition

A directed cycle is a path in a directed graph that starts and ends at the same vertex, with all edges following the direction of the arrows. It forms a loop where traversal follows the specified edge directions.

5 Must Know Facts For Your Next Test

1. A directed cycle always returns to its starting point.
2. Each edge in a directed cycle has a specific direction that must be followed.
3. A directed cycle involves at least one vertex being revisited.
4. Finding directed cycles can help identify feedback loops in systems like computer networks or ecological models.
5. The presence of a directed cycle in a graph indicates that it is not acyclic.

Review Questions

• What distinguishes a directed cycle from an undirected cycle?
• How does the presence of a directed cycle affect the properties of a graph?
• Can you provide an example of when identifying a directed cycle might be useful in real-world applications?

Related terms

Directed Graph: A graph where edges have specific directions, indicated by arrows.

Acyclic Graph:

A graph with no cycles, meaning no path exists that starts and ends at the same vertex.

Strongly Connected Component: A subgraph where there is a path between any two vertices, considering edge directions.