Most people belong to multiple social networks, both online and off. For me, each network is distinct: People from high school, who are my closest friends and whom I don't see nearly enough; smart, funny journalists I follow on Twitter, most of whom I've never met; the friends I go out with in New York, who generally prefer the sloppy gaiety of happy hour to the stuffy precision of a good cocktail bar.

My networks are a mixed bag, to say the least. But they do have a few indisputable similarities. For starters, I am less popular, on average, than the others in each of these networks, and not because I'm a very unpleasant person to be around. (Or at least I'd like to think.) Mathematically speaking, there is simply a greater chance that they have more friends than I do.

This phenomenon, first established in a landmark paper by sociologist Scott Feld in 1991, is called the "friendship paradox." And it doesn't just apply to me; it applies to all my friends. And their friends. And the friends of their friends.

Here's psychologist Satoshi Kanazawa on how the paradox works (key nugget emphasized):

If you think about it for a moment, you'll figure out the source of this seeming paradox (although this simple insight did not occur to anyone before Feld published his paper in 1991). You are more likely to be friends with someone who has more friends than with someone who has fewer friends. There are 12 people who have a friend who has 12 friends, but there is only one person who has a friend who has only one friend. And, of course, there is no one who has a friend who doesn't have any friends. Yet there is actually only one person who has 12 friends. So "12" gets counted only once when you compute the average number of friends that people have, but it gets counted 12 times when you compute the average number of friends that their friends have. Hence the seeming paradox that your friends have more friends than you do. [Psychology Today]

How this phenomenon plays out using other metrics is a question that has interested network scientists ever since. For example: What if your friends aren't just more popular than you are, but richer and happier, too? Can the same mathematical principles be applied?

We may have received our first attempt at an answer. In a new study (PDF), Young-Ho Eom at the University of Toulouse in France and Hang-Hyun Jo at Aalto University in Finland set out to evaluate if "other characteristics, such as wealth and happiness, which are not represented by the network topology," could be amplified by our fabric of connectivity.

Researchers faced a few obstacles in testing their thesis. Finding a trustworthy metric for "happiness" is difficult. (One problem: Everyone lies.) Also, not everyone was willing to open up their contact lists and bank accounts.

Instead, researchers turned to a sample set they were familiar with and had easy access to: The insular world of academia. Specifically, they looked at the the academic networks of scientists, and how often they co-authored or were cited in a scientific paper.

The thinking goes like this: The more frequently you have work published, and the more you are cited by your colleagues, the more esteemed and successful your career. It seemingly endorses all those familiar complaints: It's about who you know, talent only gets you so far, etc.

Sure enough, the paradox raises its head in this network too. If you are a scientist, your co-authors will have more co-authors than you, as reflected in the network topology. But curiously, they will also have more publications and more citations than you, too.

Eom and Jo call this the "generalized friendship paradox" and go on to derive the mathematical conditions in which it occurs. They say that when a paradox arises as a result of the way nodes are connected together, any other properties of these nodes demonstrate the same paradoxical nature, as long as they are correlated in certain way.

As it turns out, number of publications and citations meet this criteria. [MIT Technology Review]

The same network effects can be applied, the authors claim, to characteristics like wealth and happiness, the implications of which are interesting if true.

It means you aren't imagining it when it feels like all your friends are doing better than you — they really are! Such a discovery could help explain why study after study all suggest that Facebook — and the window it provides into other peoples' lives — is making us feel inadequate and unhappy.

Envy isn't a green-eyed monster. It's the odds.