It seems that every president has shaken its predecessor's hand at least once, so at most 43 handshakes. Is it possible to find a smaller (even much smaller?) chain? If someone knows a source of all the inter-presidential handshakes, I can find the smallest chain going only through presidents, but it could also go through other people.
The best I can come up with is that it might be as low as 12 handshakes, as shown below. I compiled this list assuming that when a president is elected he would seek out the advice of any/all living predecessors, meet with them and (as is customary) shake hands with them. Where possible, I have linked a picture showing the two stated presidents shaking hands or being near each other.
A couple of interesting points which help this along: Clinton met Kennedy in his youth. Grant served as a general under Lincoln, I'd bet they shook hands at some point.
There are a couple points where this list could grow; For example, Grant was only alive for a few months at the beginning of Cleveland's first term. Hopefully, somebody could find better supporting documentation for the remaining handshakes.
Based in part on previous comments in this thread, but diverging a bit at the end, I think I've got it down to seven handshakes:
If you exclude non-presidents, and use /u/F0uri3r's reasoning, I think you can do it in eight handshakes:
There's a bit of inductive reasoning in those last two steps — they're based on the assumption that candidates for senior domestic or diplomatic posts would be likely to meet or have met the president.
I would say it would involve John Tyler.
Probably something like Washington to Thomas Jefferson to Joseph Story to John Tyler to Lyon Gardiner Tyler to Lyon Tyler Jr to ? to Obama.
There's a missing link in there but I'd assume Lyon Jr. and Obama are only separated by one person since they're both living and shake a lot of hands.
So, I'm pretty confident it's 7 or less.
