title: How to get the minimum cost of disconnecting some node from each other in a graph
body: <p>In a given graph, i want to calculate the minimum cost of disconnecting some node from each other in a graph. Example: <br><img src="https://i.stack.imgur.com/KMS13.png" alt="enter image description here"> In this graph, let say i want to disconnect <code>node A</code>, <code>node C</code> and <code>node F</code> with each other by removing some edges among these nodes. i.e. by removing <code>edge A-B</code> and <code>edge F-E</code>, the nodes <code>A</code>, <code>C</code> and <code>F</code> will be disconnected. Here cost means the length of the edge which is being removed. in this example total minimum cost for disconnecting <code>Node A</code>, <code>Node C</code> and <code>Node F</code> from each other is 2+1=3.
  <br>Can somebody provide some hint. I am unable to categorize this problem, whether this is a kind of <code>shortest path problem</code> or <code>minimum spanning tree problem</code>?</p>