strongly-connected-graph

How to find Strongly Connected Components in a Graph?

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问题 I am trying self-study Graph Theory, and now trying to understand how to find SCC in a graph. I have read several different questions/answers on SO (e.g., 1,2,3,4,5,6,7,8), but I cant find one with a complete step-by-step example I could follow. According to CORMEN (Introduction to Algorithms), one method is: Call DFS(G) to compute finishing times f[u] for each vertex u Compute Transpose(G) Call DFS(Transpose(G)), but in the main loop of DFS, consider the vertices in order of decreasing f[u]

How to find Strongly Connected Components in a Graph?

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Anytime strongly connected components via Prolog

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问题 Markus Triska has reported an algorithm to determine strongly connected components (SCC). Is there a solution which determines the SCC without making use of attributed variable and that can work anytime. So that some vertices can have infinitely many edges? I am asking because I am wondering whether B-Prologs anytime tabling which they call eager can be replicated. B-Prolog determines clusters which is their name for SCC. But it has also a tabling mode where it returns tabled results eagerly.

How to reduce a strongly connected component to one vertex?

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问题 From https://algs4.cs.princeton.edu/42digraph/ Reachable vertex in a digraph. Design a linear-time algorithm to determine whether a digraph has a vertex that is reachable from every other vertex. Kosaraju-Sharir algorithm gives us the strongly connected components. Java code for that can be seen here. Reducing each SCC to a single vertex, a vertex that has outdegree zero is reachable from every other. Problem is, everyone seems to be talking about reducing a SCC without providing details.

Algorithm to check if directed graph is strongly connected

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问题 I need to check if a directed graph is strongly connected , or, in other words, if all nodes can be reached by any other node (not necessarily through direct edge). One way of doing this is running a DFS and BFS on every node and see all others are still reachable. Is there a better approach to do that? 回答1: Tarjan's strongly connected components algorithm (or Gabow's variation) will of course suffice; if there's only one strongly connected component, then the graph is strongly connected.

Algorithm to check if directed graph is strongly connected

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I need to check if a directed graph is strongly connected , or, in other words, if all nodes can be reached by any other node (not necessarily through direct edge). One way of doing this is running a DFS and BFS on every node and see all others are still reachable. Is there a better approach to do that? Tarjan's strongly connected components algorithm (or Gabow's variation) will of course suffice; if there's only one strongly connected component, then the graph is strongly connected. Both are linear time. As with a normal depth first search, you track the status of each node: new, seen but