Before going into them, whenever you are dealing with representing graphs in files, you have to decide how you are going to format them. "White color" means that the vertex hasn't been visited yet. The topological sort may not be unique i.e. The answer is that both approaches will work. 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. If there are no cycles, I assume the topological order I found is valid. Use the following approach: consider we have three colors, and each vertex should be painted with one of these colors. Thus, the above file defines a directed graph. graph can contain many topological sorts. Your function should return true if the given graph contains at least one cycle, else return false. If there is a cycle, I assume the topological order is useless. Union Find: For this question, since a child can have multiple parents, things get tricky. And if the graph contains cycle then it does not form a topological sort, because no node of the cycle can appear before the other nodes of the cycle in the ordering. Detect Cycle in a Directed Graph Given a directed graph, check whether the graph contains a cycle or not. And the answer is: If no vertex has indegree 0, we can find a cycle by tracing backwards through vertices with positive indegree; since every vertex on the trace back has a positive indegree, we eventually reach a vertex twice, and the cycle has been found. "Gray" means that we've visited the vertex but haven't visited all vertices in its subtree. Is "topological sort of an undirected graph… We have discussed a DFS based solution to detect cycle in a directed graph.In this post, BFS based solution is discussed. "Black" means we've visited all vertices in subtree and left the vertex. (Don’t use depth first search, we want just a modification of the basic topological sort.) Here's a little code for topological sort and cycle detection. It seems like your question is the following: can you use depth-first search to detect cycles in an undirected graph, or should you use topological sort instead? Steps involved in detecting cycle in a directed graph using BFS. Topological Sort: TS can be only used to directed graph. Detect cycle in a directed graph using topological sort. What about undirected graphs? Detect cycle in Directed Graph using Topological Sort , In Topological Sort, the idea is to visit the parent node followed by the child node. Topological Sort / Cycle Detection. Am I correct so far? An acyclic graph always has a topological sort. I can determine the topological sort of a directed graph using DFS algorithm. Please corect me if this is not true. The idea is to simply use Kahn’s algorithm for Topological Sorting. While I was searching for it I came across different techniques like DFS and topological sorting to detect cycle in a directed graph. 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