# How do you check if a graph contains a cycle?

## How do you check if a graph contains a cycle?

Approach: Run a DFS from every unvisited node. Depth First Traversal can be used to detect a cycle in a Graph. DFS for a connected graph produces a tree. There is a cycle in a graph only if there is a back edge present in the graph.

## How will you detect a cycle in a graph using BFS?

We do a BFS traversal of the given graph. For every visited vertex ‘v’, if there is an adjacent ‘u’ such that u is already visited and u is not a parent of v, then there is a cycle in the graph. If we don’t find such an adjacent for any vertex, we say that there is no cycle.

How do you find nodes in cycle?

What’s the most efficient way to identify all nodes that are members of a cycle in a directed graph? [duplicate]

1. Perform a depth-first search starting from an arbitrary node.
2. Push all nodes I’ve seen in a given branch into a “seen” array.
3. For each new node, check if any of its children are in the seen array.

Can BFS detect cycle in directed graph?

BFS wont work for a directed graph in finding cycles. Consider A->B and A->C->B as paths from A to B in a graph. BFS will say that after going along one of the path that B is visited.

### Does undirected graph have a cycle?

Cycle detection The existence of a cycle in directed and undirected graphs can be determined by whether depth-first search (DFS) finds an edge that points to an ancestor of the current vertex (it contains a back edge). All the back edges which DFS skips over are part of cycles.

### Does graph contain cycle?

A graph (sometimes called undirected graph for distinguishing from a directed graph, or simple graph for distinguishing from a multigraph) is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of paired vertices, whose elements are called edges (sometimes links or …

Can a cycle have 2 nodes?

Having a graph with 2 nodes is not a cycle and it cannot be a cycle because it conflicts with the rule for a set of nodes to contain a cycle. If you have 3 nodes then it is possible to have a cycle if every node has at least 2 edges.

Where DFS is better than BFS?

DFS uses Stack to find the shortest path. BFS is better when target is closer to Source. DFS is better when target is far from source. As BFS considers all neighbour so it is not suitable for decision tree used in puzzle games.

## Can a cycle repeat edges?

Cycle is a closed path. These can not have repeat anything (neither edges nor vertices). Note that for closed sequences start and end vertices are the only ones that can repeat.

## How to check if a directed graph has a cycle?

Given a Directed Graph consisting of N vertices and M edges and a set of Edges [] [], the task is to check whether the graph contains a cycle or not using Topological sort. Topological sort of directed graph is a linear ordering of its vertices such that, for every directed edge U -> V from vertex U to vertex V, U comes before V in the ordering.

How to detect cycle in graph using topological sort?

Recommended: Please try your approach on {IDE} first, before moving on to the solution. In Topological Sort, the idea is to visit the parent node followed by the child node. If the given graph contains a cycle, then there is at least one node which is a parent as well as a child so this will break Topological Order.

Is there a cycle in the recursion stack?

If a vertex is reached that is already in the recursion stack, then there is a cycle in the tree. The edge that connects the current vertex to the vertex in the recursion stack is a back edge. 