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Wolfram Alpha, a computational search engine, released a detailed report Wednesday about people’s friendships and relationship habits on Facebook.

The research is corralled from the details of more than one million people who have signed up for a free feature on the Wolfram Alpha Web site, Personal Analytics for Facebook, that uses complex algorithms to answer questions and generate reports about the social network.

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The research found that the median user has 342 friends on Facebook. This has continued to grow rapidly in recent years. But that number does not include everyone on the service, as “there are significantly more people who have almost no Facebook friends.”

The differentiating factor between people who are ultra popular on the site, and those who are Facebook loners, seems to come down to age.

“After a rapid rise, the number of friends peaks for people in their late teenage years, and then declines thereafter,” wrote Stephen Wolfram, a scientist and entrepreneur. “Why is this? I suspect it’s partly a reflection of people’s intrinsic behavior, and partly a reflection of the fact that Facebook hasn’t yet been around very long.”

The report also showed the relationship status of people across Facebook. People begin to change their relationship status to “in a relationship” in their early 20s, and then at around 27 begin to tag themselves as “engaged.” The next step, of course, is letting the world know they are married. The marriage relationships status continues to grow slowly for people in the late 20s all the way to age 60.

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One curious addition to the relationship aspects of the research found that with age, “the fraction of people who report themselves as single continues to increase for women, while decreasing for men.”

A number of teenagers tend to muddy the statistics slightly by tagging themselves as “married” at a very young age. This is often a result of a strange Facebook hack that teenagers use to note that they are best friends with someone.

Mr. Wolfram compared the data from his research to the United States census data, and found that the two were almost identical, with Facebook users and the real world marrying in their mid-20s.

Using the Facebook data, researchers were also able to determine that although Facebook’s users now total 1 billion, the majority of people on the service are young.

The research also highlights other relationship information — including how people tend to meet and tag friends into grouped clusters around school, work or personal settings, and how the geographic location of friends changes for 18-year-olds as they begin to leave their hometown and head off to college.