What do your mobile phone habits say about you? Probably more than you might imagine.

At least, that’s the suggestion from Lauri Kovanen and pals at the Aalto University School of Science and Technology, Finland. These guys have studied the 350 million calls made by 5.3 million customers over an unnamed mobile phone network during a period of 18 weeks. The primary question they ask is whether mobile phone calls are mutually reciprocated: in other words, does somebody who calls another individual receive in return as many calls as he or she makes, a phenomenon known as reciprocity.

Mobile phone calls are a particularly good way to study reciprocity because they are directed in a way that sms messages and email are not. In a mobile phone call, the caller initiates the conversation and then both parties invest a certain amount of time in the event. But afterwards there is usually no immediate reason for the recipient to call back. So it’s clear who initiated the event.

But SMS messages or e-mails are entirely different: here a conversation usually means sending a sequence of reciprocated messages and this makes it much more difficult to study reciprocity by simply counting the number of messages.

This has allowed Kovanen and company to unearth a number of interesting phenomena. For a start, the calling patterns of prepaid users is very different from those with a contract who pay later. Postpaid users tend to be more prolific, having on average 5.41 people they call.

Prepaid users, by contrast, have only 3.41 contacts on average (although the notion of “average” is a little strange here since there is a very long tail on these distributions).

Not only that but postpaid users make 10 times as many calls as prepaid users. “We can also see that prepaid users receive more calls than they make, while the most active postpaid users make more calls than they receive,” says Kovanen and company.

Prepaid users are also have more skewed relationships. Among prepaid users, the relationships where one participant makes more than 80 percent of all calls make up over 25 percent of the total.

The figures for postpaid users are far less skewed but they are greater than you’d expect from an ordinary probabilistic distribution in which each party in a relationship was just as likely to call the other.

So what’s the difference between prepaid and postpaid callers? One of the most important is probably that prepaid users are much more likely to be young people. And sociologists already know that relationships between young people tend not to be equally reciprocated.

A few years ago, the National Longitudinal Study of Adolescent Health asked US students to name up to five of their best friends. Between them, the students named 7,000 individuals but only 35 percent of the nominations were reciprocated. So perhaps it’s not suprising that a similar picture emerges from the study of mobile phone calls.

More puzzling is the skew in reciprocity in postpaid users which may not be as significant as for prepaid users but is still worthy of note.

What Kovanen and co are uncovering may be some fundamental property of human relationships; only more study will reveal that.

But the work is important for another reason: the skewed reciprocity between mobile phone users may influence other things such as the spread of ideas and information in society or, just as likely, the spread of viruses.

And that could have important implications for the way antivirus efforts are organised and directed.

Ref: arxiv.org/abs/1002.0763: Reciprocity of Mobile Phone Calls