Source: Beineke, Lowell W., and Frank Harary. "The connectivity function of a graph." Mathematika 14.2 (1967): 197-202.
If (k, l) is a connectivity pair for vertices s and t in graph G, then there are k + l edge-disjoint paths joining s and t, of which k are mutually non-vertex-intersecting.
Test the hypothesis for all small graphs (n <= 10).
Create a system where queries like the above can be executed in a distributed fashion.