Q&A: Why you have fewer friends than your friends do on Facebook

In reaching its one billion user mark Facebook may be making the world smaller, but why do you still have fewer friends than your friends do? SmartPlanet speaks with math expert Johan Ugander to find out.
Written by Christie Nicholson, Contributor

With its one billion user mark hit yesterday, Facebook is closer to its mission of making the world more connected. And it appears to be literally changing the long-held idea of six degrees of separation, which states that everyone is no more than six steps from any other person on Earth. Researchers have found that within the Facebook community, that key number shrinks to just over four steps. This is just one finding of many coming out of an enormous study of 721 million active users on Facebook led by a group at Cornell University in collaboration with Facebook's Data Science team. With such an embarrassment of social connection riches, the researchers have uncovered fascinating patterns and quirks of human and social behavior.

If you've felt not-as-popular as your friends on Facebook, you are right. Typically your friends will have about three times as many friends as you. Why? Well it has to do with math and statistics, and the research teams have proven that it plays out consistently within the Facebook network.

SmartPlanet spoke with Johan Ugander, a PhD candidate at Cornell's Center for Applied Mathematics, and asked him to explain this friendship paradox, as well as reveal other findings about our social natures from this massive study.

SmartPlanet: One of the fascinating things is that, and you got this from the Facebook data, if all the people on a four-person list came from separate social groups (eg, from your high school, or work, or family) then the likelihood of you being influenced by those people is more than twice as likely than if all the people were from the same social group (eg, all co-workers.)

Johan Ugander: Right. Facebook promises this opportunity in resolving incredibly data demanding questions in the social sciences. So we studied Facebook’s data and how millions of individuals are making decisions about joining Facebook.

And you found a very interesting quality of social decision-making, right?

Yes, we specifically looked at the invitation mechanism. Say you’re invited to Facebook, and they show you a number of different faces, faces of people already on Facebook. And the thing that really surprised us was that the dominant driving force was not how many unique social contacts that invited you.

It was some quality of those social contacts?

We found is that if there are two people that are part of this invitation community, and if those two people come from different social contexts, you’re fifty percent more likely to accept the invitation than if they’re from the same context.

So you mean that if two people are in the welcome invite to Facebook and one is from your high school context and the other is a co-worker you are twice as likely to join than if those two people were both family members?

Right. The basic motivation of this is that people that are from the same context are essentially redundant. So if your brother and sister are both recommending you a book, you don’t really take them as independent sources of information. But if your co-worker and your siblings recommend you a book, that’s a much stronger recommendation, because now it’s sort of reached you from two independent directions.

Fascinating. What are the practical implications of this?

With health practices, researchers are trying to figure out how to convince people to start using good health practices. Another obvious application is to help business spread ideas. And a recent study where the Facebook team studied the spread of voter participation, and it also showed that there is a big social component to voting.

Can you talk a bit more about Facebook’s research teams and what their motivations are?

Facebook has a research group called the Data Science team that helps to guide the product to its next levels. The Science Team has really grown since 2010.

And you started working with them in 2010 right?

One of the big papers that we put out in 2010 is this large-scale study where we asked a wide range of empirical questions about Facebook as a social network.

We were sitting on the largest social network data set, this treasure trove of data. So we asked a lot of the same questions social researchers have asked before, but now we were asking at a Facebook scale.

And what was one of those questions?

Well it has to do with the famous notion of six degrees of separation. With Facebook we have something resembling the complete graphic world, we have ten percent of the world’s population.   So how far apart are people?  Is it six degrees?

And was it?

No. In fact the average distance between any two people on Facebook was 4.74. But also we found these results had been shrinking over the the past three years, since 2007, the average distance between two people has been shrinking. This is related to Facebook’s mission of making the world more open and connected. A lot of people at Facebook were happy to see this.

Yes, Facebook has actually making the world smaller, by allowing relationships to flourish online, globally.

Another question that we wanted to ask was this notion of your friends always have more friends than you.

Right. That is fascinating, that no matter what, on Facebook your friends on average, will always have more friends than you have. It might seem depressing.

It’s called the “friendship paradox”. If you look across your friends, surprisingly often you have fewer friends than your friends do. And this is derived from a mathematical theorem.

And you found that the math worked in reality?

Yes we found that 93 percent of Facebook users have fewer friends than their friends. So it’s a mathematical fact, not something one should be depressed about.

Consider this metaphor: It happens for the same reason that when you go to the gym, you see only the fit people, and when you look at your friends on Facebook you see only people who are social.

You mentioned that Facebook users have an average number of 190 friends. But their friends average 635 friends. Now, when you say their friends average, are you talking about their total number of friends or are you talking about each individual friend added up? This is where it gets tricky.

Exactly, this is where it gets tricky. If you select a person at random and you get an average number of friends at 190. But if you look at a random friend of a random user, you’re biasing your selection towards people who have a lot of friends. You’re much more likely to hop to somebody who has a lot of paths leading to them. Somebody who has ten thousand friends is going to show up much more in your sample than somebody who only has two friends.

The gym metaphor helps here.

Right,  if you go to the gym you’re only seeing the people who go to the gym often. The couch potatoes are only going to the gym once a month, so on your average visit you’re not going to see them, whereas you’re going to see the person who’s there everyday.  And you might feel bad about your physique.

What would be a practical implication for the “friendship paradox”?

Well for Facebook there are implications. These factors of friends grow very quickly. Take a person with a 100 friends, and you think OK, their friends have about a hundred friends each, so you’d expect them to have 10,000 friends of friends, which is 100 x 100. But in reality a person with a hundred friends has twenty-seven thousand friends of friends, close to three times more than you would expect. This paper provided Facebook's engineering people information on how some of these properties behave on Facebook.

What are Facebook's goals with this research arm?

The Data Science team has an ambition to do a complete overhaul of these questions in social science and social psychology because it has a huge treasure trove of data. The research is useful for the design of products and recommendations that Facebook offers.

But on the academic side, the social science hypotheses that have been around for decades we can now get numbers for. And there’s a long list of studies that we’d like to run.

This post was originally published on Smartplanet.com

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