I have come to read [this](https://stackoverflow.com/questions/14305236/minimal-addition-to-strongly-connected-graph) stackoverflow post. It basically asks this-`I have a set of nodes and set of directed edges between them. The edges have no weight. How can I found minimal number of edges which has to be added to make the graph strongly connected?`↵
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[This](https://stackoverflow.com/a/14318315) answer gives a solution to this problem↵
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It's a really classical graph problem.↵
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1. Run algorithm like Tarjan-SCC algorithm to find all SCCs. Consider each SCC as a new vertice, link a edge between these new vertices according to the origin graph, we can get a new graph. Obviously, the new graph is a Directed Acyclic Graph(DAG).↵
2. In the DAG, find all vertices whose in-degree is 0, we define them {X}; find all vertices whose out-degree is 0, we define them {Y}.↵
3. If DAG has only one vertice, the answer is 0; otherwise, the answer is max(|X|, |Y|).↵
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I am not been able to prove the third point. How is the answer "max(|X|, |Y|)"? Can anyone help me?↵
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Edit: I need this to solve this lightoj [problem](http://lightoj.com/volume_showproblem.php?problem=1210).
↵
[This](https://stackoverflow.com/a/14318315) answer gives a solution to this problem↵
↵
It's a really classical graph problem.↵
↵
1. Run algorithm like Tarjan-SCC algorithm to find all SCCs. Consider each SCC as a new vertice, link a edge between these new vertices according to the origin graph, we can get a new graph. Obviously, the new graph is a Directed Acyclic Graph(DAG).↵
2. In the DAG, find all vertices whose in-degree is 0, we define them {X}; find all vertices whose out-degree is 0, we define them {Y}.↵
3. If DAG has only one vertice, the answer is 0; otherwise, the answer is max(|X|, |Y|).↵
↵
I am not been able to prove the third point. How is the answer "max(|X|, |Y|)"? Can anyone help me?↵
↵
Edit: I need this to solve this lightoj [problem](http://lightoj.com/volume_showproblem.php?problem=1210).
