This graph is based on an idea by J.H.Conway, as described by her biographer Siobhan Roberts. He was reportedly very happy to meet Cecilia Tanner, because this reduced his handshake distance to Cantor to only two handshakes.
I loosely define "handshakes" as a personal introduction made in person, face to face. In current western cultures, this is usually done by a handshake, but the exact manner itself varies by region and times. In Japan, for example, a "handshake" would actually be a bow gesture; and, not long ago, even close associates would not perform an actual handshake.