Six Degrees of Kevin Bacon
There are at least 3 ways to get "2 degrees of separation" in movies between me and Kevin Bacon, so I have a Bacon number of 2. Whoo hoo! We're practically bro's. Only 20% of actors on IMDb have a Bacon number of 2 or less.
For idle curiosity, you can go to The Oracle Of Bacon and enter any two actors and it will give you a list of movies that connect them. Of course, it is patently useless trivia.
For those who don't know, this is a variation on the casual observation that it takes a surprisingly few number of connections between any two random people, with almost everyone within "six degrees of separation" ― which inspired the title of a Will Smith movie. Depending on the group, the maximal distance between people might be even smaller: A 2016 Facebook report found that for 1.59 billion in their network it's closer to 3½ degrees.
The "Bacon Number" meme is about finding how many movies connect a given actor to super-productive actor Kevin Bacon. The number of movies is that actor's "degrees of Bacon" or, more simply, their Bacon number. Note: while Kevin Bacon has a lot of impressive credits, there are some 400 other actors who are even more connected, like Sean Connery and Al Pacino. Kevin was just lucky to be noticed first.
It only takes a few super-connected people like this to tie together a network. You can also look at relationships between you and an extremely popular person as an indicator of how "close" you are to the center of the network (c.f., a log of the network connections). The closer you are to that person, the closer you are to the network center and, therefore, the closer you are to all persons in the network. Facebook uses something similar in their social graph algorithms to prioritize, c.f., popularize, items for your news feed. Since I'm already only 3 or 4 people away from 1.59 billion on Facebook alone, I think I'm good.