Facebook, in collaboration with researchers at the Università degli Studi di Milano, has released two studies of the Facebook social graph. The studies measured how many friends people have, and found that this distribution differs significantly from previous studies of large-scale social networks. The studies also found that the degrees of separation between any two Facebook users is smaller than the commonly cited six degrees, and has been shrinking over the past three years as Facebook has grown. Finally, while the entire world is only a few degrees away, your friends are most likely to be of a similar age and come from the same country.

In the studies, performed earlier this year, Facebook examined all 721 million active users of its social networking site, which happens to be more than 10 per cent of the global population, with 69 billion friendships among them. To date, these are the largest social network studies ever released, says Facebook.

How many friends?

An important basic view of any social network is the cumulative degree distribution, which shows the percentage of individuals that have less than a given number of friends. As you can see above, only 10 per cent of people have less than 10 friends, 20 per cent have less than 25 friends, while 50 per cent (the median) have over 100 friends. Meanwhile, because the distribution is highly skewed, the average friend count is 190.

However, the studies reveal that the distribution is not nearly as skewed as earlier studies of social networks have suggested.

At first glance, the median friend count on Facebook — 100 — may seem surprisingly low. But no, your friends are not atypically social – a classic paradox regarding social networks dictates that, for most people, the median friend count of their friends is higher than their own friend count. On Facebook, that’s the case for 84 per cent of our users. Why? Scott Feld wrote about this phenomenon in his 1991 paper ‘Why Your Friends Have More Friends than You Do’, showing that the same phenomenon dictates that college students typically find that their classes to be larger than the average class size, and that when sitting on an airplane, it will typically be more crowded than the average occupancy. These effects all arise because for people, classes, and flights to be popular, you must be much more likely to choose them. So you shouldn’t feel bad if it seems like all your friends are more popular than you: it appears this way to most of us.

Four Degrees of Separation

The idea of ‘six degrees of separation’ — that any two people are on average separated by no more than six intermediate connections — was first proposed in 1929 in a short story by Hungarian author Frigyes Karinthy, and made popular by the John Guare play and movie, Six Degrees of Separation. The idea was first put to the test by Stanley Milgram in the 1960’s. Milgram selected 296 volunteers and asked them to dispatch a message to a specific individual, a stockholder living in the Boston suburb of Sharon, Massachusetts. The volunteers were told that they couldn’t send the message directly to the target person (unless the sender knew them personally), but that they should route the message to a personal acquaintance that was more likely than the sender to know the target person. Milgram found that the average number of intermediate persons in these chains was 5.2 (representing about 6 hops). The experiment showed that not only are there few degrees of separation between any two people, but that individuals can successfully navigate these short paths, even though they have no way of seeing the entire network.

Using state-of-the-art algorithms developed at the Laboratory for Web Algorithmics of the Università degli Studi di Milano, the Facebook studies were able to approximate the number of hops between all pairs of individuals on Facebook. According to the results, six degrees actually overstated the number of links between typical pairs of users: While 99.6 per cent of all pairs of users are connected by paths with 5 degrees (6 hops), 92 per cent are connected by only four degrees (5 hops). And as Facebook has grown over the years, representing an ever larger fraction of the global population, it has become steadily more connected. The average distance in 2008 was 5.28 hops, while now it is 4.74.

Thus, when considering even the most distant Facebook user in the Siberian tundra or the Peruvian rainforest, a friend of your friend probably knows a friend of their friend. When limited to a single country, be it the US, Sweden, Italy, or any other, the ananlysis found that the world got even smaller, and most pairs of people are only separated by 3 degrees (4 hops). Facebook however says these numbers are not directly comparable to Milgram’s numbers ; his subjects only had limited knowledge of the social network, while Facebook has a nearly complete representation of the entire thing.

Your friends and you.
The study found that 84 per cent of all connections are between users in the same country. But this isn’t the only dimension along which people tend to cluster. The study also revealed that people tend to have a similar, albeit typically smaller, number of friends as their neighbors, and tend to be about the same age. Somewhat surprisingly, even for individuals aged 60, the distribution of their friends’ ages is sharply peaked at exactly 60.

Edited: 04-28-13