How can I prove the “Six Degrees of Separation” concept programmatically?

Question

I have a database of 20 million users and connections between those people. How can I prove the concept of \"Six degrees of separation\" concept in the most efficient w

Answer 1

I think the most efficient way (worst case) is almost N^3. Build an adjacency matrix, and then take that matrix ^2, ^3, ^4, ^5 and ^6. Look for any entries in the graph that are 0 for matrix through matrix^6.

Heuristically you can try to single out subgraphs ( large clumps of people who are only connected to other clumps by a relatively small number of "bridge" nodes ) but there's absolutely no guarantee you'll have any.