Algorithm to find neuralgic point2 in a large graph
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Assume i have a large arbitrary graph of connected vertices like the following. Assume these are network connections. Some connections (colored in red) are much more serve to damage then others. If two red connections fail, many points have no more connection to members of the remaining island.

How can find these neuralgic connections?

Is there a existing algorithm for that?

![graph sample][1]


  [1]: http://i.stack.imgur.com/Pk40X.jpg