The minimum number
in a graph
between two people
. A way of referring to the 6 degrees of separation
idea. If A knows B and B knows C then the handshake number of A and B is 2 (unless A also knows C, in which case it would be 1).
The phrase can also refer to the overall minimum number of steps to connect any two people in a specified group. I think that the handshake number for Canada is about 5.
Another application of this idea is the Erdos number project.