I'm dealing with tables that show connectivity within a network. Can anyone point me toward a technique for ordering the rows and columns so that nodes that are connected tend to be close to each other in the table?
For example, if I had a network like this (connections are directional), the structure isn't immediately obvious; it just looks random.
1 2 3 4 5 1 x x 2 x 3 x x 4 x x 5 x
But if you re-order the columns and rows this way, the structure is clear; you can see some organisation in the network.
2 4 5 3 1 2 x 4 x x 5 x 3 x x 1 x x
Of course, I'm dealing with larger tables, with ~1024 nodes. I could just code up something that tries to find the arrangement with the minimal average distance between connected nodes by some general-purpose method like gradient descent. But perhaps there's a technique that's particularly suited to this type of problem?