Three and a half degrees of separation | Hacker News Reader

Three and a half degrees of separation

research.facebook.com

141 pointscanistr62 comments

>Each person in the world (at least among the 1.59 billion people active on Facebook) is connected to every other person by an average of three and a half other people.

This is a big deal, and always a fascinating result, but the other 5.5 billion cannot be merely discounted. 1.6 billion is over 22% of the global population, which makes for a very good sample set, but it is definitely biased. I may be 3.3 degrees away from "everyone on Facebook" but that isn't everyone. Almost by definition, those 5.5 billion people not on Facebook should be harder to reach, requiring many more steps.

Results from Weibo would be an interesting comparison.

> How connected is the world? ... we've crunched the Facebook friend graph and determined that the number is 3.57

Agreed. this statement is presumptuous and self-aggrandizing and just incorrect. They should re-word this sentence and its implication.

And yet right beneath that they say;

(at least among the 1.59 billion people active on Facebook)

that parenthetical is not enough for me

You must be fun at parties.

about as fun as i am here apparently

That last comment was hysterical. You can come to my party.

if it's in oakland i'll bring the 40

to your point, imagine the bed-ridden mother of a tribesman of a remote village in Sub-Saharan Africa and you easily tack on 2 more degrees of separation (the tribesman who has infrequent contact with a nearby city and then his senior-aged mother).

It's an average, not a maximum.

But that's cheating, isn't it? I'm quite sure the quote the article starts with that mentions six degrees means that that is the maximum.

To be realistic, too, the original "six degrees of separation" did not take into account this international context.

Yes it did. "Gondolier from Venice" is right there in the article.

We're considering connections analogus to Facebook friendships, not currently open lines of communication. The mother, having lived a long life, likely knows hundreds of people in the village and the next few over (several of whom have moved to a number of different cities, a few quite far), so her son doesn't automatically tack on a degree of separation.

Not the point.

All it takes is one real example and you add to everyone.

IE a remote mother who has had a child is an automatic + one.

A 13 year who's been born remote and has a child remotely is plus two.

I could imagine a child this age only having ever met village members somewhere creeping off to have a baby.

Facebook is cheating by averaging.

This number is pretty deceiving. The degree of separation is meaningful only if you can actually leverage your relationship to pass on the message in the graph. In FB graph, I would think that vast number of relationships are not mutual, active or "leveragible".

Here's better way to find degrees of separation:

Assign each relationship some weight. For example, if two people haven't interacted mutually with each other than weight is much higher and vice versa. Now compute all pairs shortest path and take average. This would give a much better picture of actual degree of separation.

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".

> 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.

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.

Reminds me of how NSA uses 3 degrees to target your communications: http://www.theguardian.com/world/interactive/2013/oct/28/nsa...

That's exactly what I thought this article was about until I saw its source. I mildly shuddered at the thought I was about to see another revelation of how twisted and overly broad their targeting was. In a rare event, Facebook was a relief haha.

Why is Facebook confusing the EVERYBODY connected within X steps with AVERAGE connection distance?

Are they deliberately lying, or incompetent?

6 degrees hasn't shrunk. Facebook is merely counting something else. Why doesn't anyone point this out? I feel like I'm taking crazy pills.

It's not clear to me exactly what you mean. Could you elaborate? Or provide an example?

From wikipedia, emphasis my own: "Six degrees of separation is the theory that everyone and everything is six or fewer steps away, by way of introduction, from any other person in the world".

This does not mean that any two randomly selected people will, on average, be separated by six degrees. It is the (theorized) maximum of the separation between all possible combinations of two people on Earth.

Facebook calculated a different metric: the average separation. And at this, they only calculate it among Facebook's own users - not all living people. Yet they present their findings as if they are directly applicable to the initial problem statement, which they aren't.

I mean, some groups of people on earth are uncontactable or their existence is unknown (see Sentinelese, people in the Amazon). So you have to make a compromise at some point. The choice of percentile is somewhat arbitrary.

Alternatively, you could limit your population of interest to the largest group of people that can all find a route to each other. In practice, this just boils down to excluding "uncontacted/unknown" peoples.

It's a bit different than choosing a percentile to target, and also a bit less arbitrary, in my opinion.

If they're going to be referencing the six degrees of separation theory, what they should really be doing is making the same assumptions that were used in that theory (whatever those were).

I already know how I'm connected to the big Z, and amusingly enough it is close to their 3.5 degrees of separation. My ex-girlfriend (1) has an aunt (2) that has a cousin who is Priscilla (3) who is wife of Z (4).

We'll meet someday Z! I just have to patch up things with my ex..

Using Facebook friendships as the connection metric like the link does, I think the vast majority of the tech industry in SF is within two or three degrees.

(I've got mutual "friends" with the guy.)

I suppose, but I'm not from SF. I'm originally from CT then went to school in Boston, and met my ex who shares same hometown as Priscilla.

Shockingly, most of the tech industry does not live in SF.

You can shorten it up a bit: her aunt’s cousin is her cousin once removed.

Haha, yes because that reads easy. I'm all for being succinct, but the point is to get the message across in a light-hearted, simple manner by using one hop at a time. What you said wrote sounds scientific and cold.

I always thought “once removed” sounded funny, because it’s rarely used in practice enough that I pretty much only hear it in gags about convoluted relationships.

You think it sounds funny for a reason :)

I think that it's an awkward pairing that needs context. You're immediately thinking "once removed from what?" and then scanning for what it is. This can be a burdensome way to end a sentence. Better to build up to something than to force the listener to look backwards and reconstruct IMO.

I don’t know what you’re talking about. “Once/twice/thrice removed” means “removed by one/two/three generations”, where “removed” has the sense of “separated”. “From what?” is the wrong question.

I'm annoyed I didn't know that. I read it as once separated, and got the overall message, but was part of the reason I found it so funny to read. Now that I've built that association, I guess it's simpler.

It's weird I'm a big talker and always reading things and never came across that in a way that I memorized it. I appreciate you explaining it to me.

The original question wasn't the average separation, it was the number of degrees to connect everybody. Looking at that distribution graph it looks like 6 is about right. To some significance anyways, I'm sure the distribution tail goes on for a ways.

It'd be super interesting to see degrees of separation within particular communities. e.g. I live in a college town with a population of about 65,000, something like 25,000 of those are college students and "don't count" due to their transient nature. As a result, it seems like everyone knows everyone here, despite the 40,000 non-transient population. I'd guess at somewhere around 2 - 2.5 degrees, but it'd be interesting to know the actual.

Cool, but a more meaningful number concerning the original meaning of "six degrees of separation" than the average of the average of the degrees of separation between each individual and everyone else would be the average of the average of the 90th, 95th, 99th etc percentiles of the degrees of separation between each individual and the most distantly separated other individuals in the graph (maybe excluding outliers who only have a few Facebook friends).

Alright, here's where I need people strong in statistics to correct me if I'm wrong as I learned it a while back. If I'm right, then this is another misuse of math to push some BS result. If I'm wrong, then it's meaningful in some way maybe. So, here is two claims about averages:

1. The average of a diverse group means something for an individual. Like in this article where they connect individuals to average degree of separation.

2. Averages, due to their nature, don't mean anything for an individual. They're mainly good for identifying and tracking trends. So, no connection could be made here.

A pro told me that No 2 is the case a long time ago. It made more sense given the data I've looked at as well in terms of example problems and reports. Need more peer review on that as statistics is kind of opinionated on how its applied. If No 2 is true, then this report is more BS that's too common and the comments here become really amusing (or sad if one is an education reformer).

Reminds me of a thing we worked on some time ago:

http://blog.stephenwolfram.com/2013/04/data-science-of-the-f...

Unfortunately the degrees of separation is not something we could ever have computed with the limited data we had.

I wonder how many of the paths are shortened through fake 'catfish' accounts?

I've always been curious about facebook scaled their "people you may know feature". Everything I've read suggests that they use contact list information uploaded by other users to introduce connections in the social graph. What I'm curious about is how they compute the intersection of the large sets that result, for a lot of people, in real time.

I wonder if this is the lower bound. The 0, 1 or 2 degree of average separation doesn't make much sense so the lower bound must be 3?

I would really like to know who is the farthest person from Z on facebook, or at least what their distance is.

How does this work if the graph isn't connected? Like if there are people who are only friends with each other and no one outside their group. Surely out of a billion people, there must be some people like that on facebook.

> In our implementation, at each step each person sends a bitwise ORed hash value to all his friends.

I didn't follow how ORing the hash is supposed to work or what it is meant to do. Anyone know?

Hey, since we practically know each other, could I borrow $20?

Thanks!

hey, its me, your brother

did they disclose the standard deviation or spread?

Not in figures, but a graph was given in the article that shows the sample distribution.

That is the distribution of the average degrees of separation for each person. What would be useful is the distribution of distributions of the degree of separation between each person and every other person.

Man I'd love to sneak a peek at what else Facebook Research can do. Having all of FB as a dataset would be endlessly fascinating.

Does being "friends" with a celebrity count?

Just a Facebook advertisement, nothing to see, move on...

This is essentially true, but some may still be interested in the results.

Reply on news.ycombinator.com