title: How to merge nodes given an adjacency matrix
body: <p>I have an adjacency matrix, and I can't seem to find a quick way to combine multiple nodes to know what the final number of "super-nodes" are. I thought an easy solution was to essentially compute the sum of the upper triangular part of the adjacency matrix, and subtracting the total amount of nodes minus the previous sum would give me the answer, but it looks a bit more tricky.</p>
  
  <p>Suppose:</p>
  
  <p>I have 6 nodes from 1 to 6:
  Nodes 1,2,3 are connected all to each other.
  Nodes 4 and 6 are connected to each other,
  Node 5 is not connected to anything.</p>
  
  <p>At this point it seems trivial that of the 6 initial nodes I will only have 3 remaining super nodes. Now the problem by using my method before is that suppose the first super-node is connected like this:
  1 to 2
  2 to 3, 
  but not 1 to 3 directly. (even though they merge).</p>
  
  <p>Here sum(upptriangle(Adj))=3 works, but for the first case I am adding a "dummy node" (the connection 1-3) outputs: sum(upptriangle(Adj))=4, and this type of connection should not affect the final result.</p>
  
  <p>Is there a standard algorithm I am missing, to solve this problem (and compensate for overcomplete of non fully connected sub-graphs?), instead of iteratively going over every node to see if it's been merged? </p>
  
  <p>In other words, is there a fast computation of node merging that I can get only from the adjacency matrix?</p>