The topological sort may not be unique i.e. Before going into them, whenever you are dealing with representing graphs in files, you have to decide how you are going to format them. The answer is that both approaches will work. The idea is to simply use Kahn’s algorithm for Topological Sorting. An acyclic graph always has a topological sort. Steps involved in detecting cycle in a directed graph using BFS. Minimum time taken by each job to be completed given by a Directed Acyclic Graph Hard Given a Directed Acyclic Graph having V vertices and E edges, where each edge {U, V} represents the Jobs U … Detect Cycle in a Directed Graph Given a directed graph, check whether the graph contains a cycle or not. 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. If there is a cycle in a directed graph, then you can detect this by running a depth-first search over the graph. If there are no cycles, I assume the topological order I found is valid. 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. Your function should return true if the given graph contains at least one cycle, else return false. 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 using topological sort. graph can contain many topological sorts. I can determine the topological sort of a directed graph using DFS algorithm. So, initially all vertices are white. My union find code only get 38/47 test cases passed. 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. Union Find: For this question, since a child can have multiple parents, things get tricky. Thus, the above file defines a directed graph. "Gray" means that we've visited the vertex but haven't visited all vertices in its subtree. (Don’t use depth first search, we want just a modification of the basic topological sort.) "White color" means that the vertex hasn't been visited yet. 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? Use the following approach: consider we have three colors, and each vertex should be painted with one of these colors. Here's a little code for topological sort and cycle detection. Topological Sort: TS can be only used to directed graph. If there is a cycle, I assume the topological order is useless. 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