That's exactly the original purpose of Orkut, the (almost defunct) original Google social network site. Orkut Buyukkokten (the Google employee that came with the idea on his 20% paid "free time") was the "Kevin Bacon" and the breadcrumbs of the site used to show the smallest paths between you and Orkut.
It was a fun experiment in the beginning because not only the path between you and Orkut was drawn, but the path between you and anyone you looked at the profile.
But then, when the first batch of geeks (who else, considering Orkut invited his geek friends of Stanford and Google first) started inviting the first batches of "civilians", in a couple of generations the experiment was not viable anymore because of the sheer amount of processing power needed to calculate the paths, the expansion of the network and the commercialization of the content.
Fun days were those when a social network by geeks, for geeks thrived (with lasers!).