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More than a million people have now used our Wolfram|Alpha Personal Analytics for Facebook. And as part of our latest update, in addition to collecting some anonymized statistics, we launched a Data Donor program that allows people to contribute detailed data to us for research purposes.
A few weeks ago we decided to start analyzing all this data. And I have to say that if nothing else it’s been a terrific example of the power of Mathematica and the Wolfram Language for doing data science. (It’ll also be good fodder for the Data Science course I’m starting to create.)
We’d always planned to use the data we collect to enhance our Personal Analyticssystem. But I couldn’t resist also trying to do some basic science with it.
I’ve always been interested in people and the trajectories of their lives. But I’ve never been able to combine that with my interest in science. Until now. And it’s been quite a thrill over the past few weeks to see the results we’ve been able to get. Sometimes confirming impressions I’ve had; sometimes showing things I never would have guessed. And all along reminding me of phenomena I’ve studied scientifically in A New Kind of Science.
So what does the data look like? Here are the social networks of a few Data Donors—with clusters of friends given different colors. (Anyone can find their own network usingWolfram|Alpha—or the
SocialMediaData function in Mathematica.)
So a first quantitative question to ask is: How big are these networks usually? In other words, how many friends do people typically have on Facebook? Well, at least for our users, that’s easy to answer. The median is 342—and here’s a histogram showing the distribution (there’s a cutoff at 5000 because that’s the maximum number of friends for a personal Facebook page):
But how typical are our users? In most respects—so far as we can tell—they seem pretty typical. But there are definitely some differences. Like here’s the distribution of the number of friends not just for our users, but also for their friends (there’s a mathematical subtlety in deriving this that I’ll discuss later):
And what we see is that in this broader Facebook population, there are significantly more people who have almost no Facebook friends. Whether such people should be included in samples one takes is a matter of debate.
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But so long as one looks at appropriate comparisons, aggregates, and so on, they don’t seem to have a huge effect. (The spike at 200 friends probably has to do with Facebook’s friend recommendation system.)
So, OK. Let’s ask for example how the typical number of Facebook friends varies with a person’s age. Of course all we know are self-reported “Facebook ages”. But let’s plot how the number of friends varies with that age. The solid line is the median number of friends; successive bands show successive octiles of the distribution.