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Say there is a graph in which every node is connected to every other by some path. How would i find the particular nodes, which if removed would lead to some of the nodes NOT being connected to all the other points?

I think DFS needs to be used. But i don't undertsand how.

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You are basically trying to find cut vertices in a connected graph. This is a common problem, eg. see See http://www.geeksforgeeks.org/articulation-points-or-cut-vertices-in-a-graph/

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