> This number is pretty deceiving.

I don't see how. Even if you think the ties are quite weak, they undoubtably exist.

> In FB graph, I would think that vast number of relationships are not mutual, active or "leveragible".

Really? Unlike Twitter, I think Facebook actually emphasizes mutual friendships. (There's no one-way followers.)

I have around 1,500 friends on Facebook and that seems like a pretty high number. But I do know all of them, at least in passing, to the extent that I'd be willing to pass along a message for one of them.

Separation calculations aren't about extracting big favors, they're about finding minimal ties. One of the original experiments was literally just passing along a letter. [1]

[1] https://en.wikipedia.org/wiki/Small-world_experiment

> Really? Unlike Twitter, I think Facebook actually emphasizes mutual friendships. (There's no one-way followers.) [emphasis added]

I don't disagree with you, but to the parenthetical: I've unfollowed plenty of people. They're still in my friend list, but I never see their posts because they were too annoying. It's not strictly one-way like with Twitter, but it's close.

Isn't that almost the opposite of Twitter though?

They're people who you want to be connected to for some reason (often a real-life connection) but you don't particularly enjoy their content. As opposed to Twitter, where you will follow people you don't know because they share content you enjoy.

Those people are still (almost certainly) following me, but I'm not following them (evidenced by their comments to my infrequent postings). But unlike Twitter, that's not the default. Twitter: default one-way, two-way requires effort. Facebook: default two-way, one-way requires effort. You wrote that there are no one-way followers. I was simply trying to point out that it was possible to end up in that situation.

The connection is often more formality than anything else (we game together, play soccer together, blood-relations, etc.). And they seem to like my posts, so they're following me, but I don't care for theirs and unfollow them.

The real issue is more that those looser friendships are more common than you’d notice (because the NewsFeed algorithm hides them by design) and because they tend to be over-represented in the great diagonals and bridges, the connections that make that number (aka the graph average diameter) much smaller. Having many friends is, paradoxically, correlated with fairly strong weak ties on average; isolate people have few close friends, but they generally can’t trust their few distant friends as much. Having half of the network as those isolated nodes increase the average quite substantially if you exclude their distant ties.

There is also a non-negligible likelihood that those traversals go often through certain spam accounts that span strangers.

I don't disagree with your point. But FB does allow one way following (you can subscribe to most users public posts).

True, but those aren't included in this analysis.

I believe they determined their methodology on past similar studies (at least they compared their results, so I would hope they used the same methodology for determining a degree). The degree of separation just asserts that there exists a friend 1 who is somehow connected to another person (and on average some distance from any other person). It makes no claim on the quality of those connections.

Also, the assumption that because two people have interacted means those relationship are easier to leverage isn't substantiated. I'm sure the result would be interesting, but it wouldn't necessarily be "more correct".

Totally agree.

I'm Facebook friends with politicians, athletes, college student body officers, amongst others that I've never met and are obvious common connections for most in my area.