# Graph – Detect Cycle in a Directed Graph

**Objective**: Given a directed graph write an algorithm to find out whether graph contains cycle or not.

**Example**:

**Approach**:

Graph contains cycle if there are any back edges. There are two types of back edges as seen in the example above (marked in red)

- Edge from a vertex to itself. Self loop. (4-4)
- Edge from any descendent back to vertex.

Use DFS(Depth-First Search) to detect the back edge

- Do the DFS from each vertex
- For DFS from each vertex, keep track of visiting vertices in a recursion stack (array).
- If you encounter a vertex which already present in recursion stack then we have found a cycle.
- Use visited[] for DFS to keep track of already visited vertices.

**How different is recursion stack[] from visitied [].**

- Visited[] is used to keep track of already visited vertices during the DFS is never gets
- Recursion stack[] is used from keep track of visiting vertices during DFS from particular vertex and gets reset once cycle is not found from that vertex and will try DFS from other vertices.
- See the code from more understanding.

**Time Complexity: O(V+E)**

**Code**:

**Output**:

is Cycle present: True