
Three and a half degrees of separation - canistr
https://research.facebook.com/blog/three-and-a-half-degrees-of-separation/
======
Amorymeltzer
>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.

~~~
awl130
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).

~~~
mseebach
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.

~~~
aaron695
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.

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sytelus
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.

~~~
morgante
> 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](https://en.wikipedia.org/wiki/Small-world_experiment)

~~~
Jtsummers
> 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.

~~~
morgante
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.

~~~
Jtsummers
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.

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lurchpop
Reminds me of how NSA uses 3 degrees to target your communications:
[http://www.theguardian.com/world/interactive/2013/oct/28/nsa...](http://www.theguardian.com/world/interactive/2013/oct/28/nsa-
files-decoded-hops)

~~~
nickpsecurity
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.

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knorker
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.

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

~~~
wallacoloo
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.

~~~
alextgordon
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.

~~~
wallacoloo
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).

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joslin01
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..

~~~
akavi
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.)

~~~
joslin01
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.

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guelo
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.

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matheweis
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.

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mwhite
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).

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nickpsecurity
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).

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

[http://blog.stephenwolfram.com/2013/04/data-science-of-
the-f...](http://blog.stephenwolfram.com/2013/04/data-science-of-the-facebook-
world/)

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

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

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tadkar
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.

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sytelus
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?

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

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imh
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.

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foobarqux
> 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?

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

Thanks!

~~~
mmanfrin
hey, its me, your brother

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awl130
did they disclose the standard deviation or spread?

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

~~~
mwhite
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.

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cwe
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.

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Animats
Does being "friends" with a celebrity count?

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

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

