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Merge pull request #741 from pirateksh/patch-1
Improved Language of Algorithm Explanation
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src/graph/strongly-connected-components.md

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@@ -34,7 +34,7 @@ There are two main different cases at the proof depending on which component wil
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Proved theorem is **the base of algorithm** for finding strongly connected components. It follows that any edge $(C, C')$ in condensation graph comes from a component with a larger value of $tout$ to component with a smaller value.
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If we sort all vertices $v \in V$ by decreasing of their exit moment $tout[v]$ then the first vertex $u$ is going to be a vertex from "root" strongly connected component, i.e. a vertex that no edges in a condensation graph come into. Now we want to run such search from this vertex $u$ so that it will visit all vertices in this strongly connected component, but not others; doing so, we can gradually select all strongly connected components: let's remove all vertices corresponding to the first selected component, and then let's find a vertex with the largest value of $tout$, and run this search from it, and so on.
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If we sort all vertices $v \in V$ in decreasing order of their exit time $tout[v]$ then the first vertex $u$ is going to be a vertex belonging to "root" strongly connected component, i.e. a vertex that has no incoming edges in the condensation graph. Now we want to run such search from this vertex $u$ so that it will visit all vertices in this strongly connected component, but not others; doing so, we can gradually select all strongly connected components: let's remove all vertices corresponding to the first selected component, and then let's find a vertex with the largest value of $tout$, and run this search from it, and so on.
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Let's consider transposed graph $G^T$, i.e. graph received from $G$ by reversing the direction of each edge.
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Obviously, this graph will have the same strongly connected components as the initial graph.

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