# VertexConnectivity and FindVertexCut disagree [duplicate]

I'm trying to use Mathematica to compute the minimal vertex cut for graphs. From what I understood, VertexConnectivity of a graph should correspond to the number of vertices in the minimal vertex cut.

However, when I use Mathematica 9.0 on a graph, I get a VertexConnectivity of 1, but the minimal cut computed by Mathematica has 33.

This seems strange! Is this a bug, or am I missing something? Any help would be appreciated!

Here's a link to the text used to generate the graph which I am testing: http://pastebin.com/WWk0Gk8G VertexConnectivity and FindVertexCut are the functions I'm using.

Regards, Dave

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• VertexConnectivity is buggy in v9, unfortunately. The correct answer is 33, not 1. I marked as a duplicate of the thread discussing this. You can either upgrade to v10 (which has this fixed) or use igraph as a workaround (as described in the link). – Szabolcs Dec 7 '14 at 16:42
• Thanks for the help! Strange that such a bug managed to get through. – Dave Dec 9 '14 at 12:29

You may see that removing a single vertex doesn't disconnects your graph. It's a bug,as noted in the comments:

And @@ Thread[ Length /@  ConnectedComponents /@ (VertexDelete[g, #] & /@ VertexList@g) == 1]

(*  True *)