The old saying that opposites attract now has some mathematical validity, at least according to a new research pre-print made available this week. The paper, by Lars Backstrom of Facebook and Jon Kleinberg of Cornell University, looks at Facebook friend network data and link. The authors attempt to predict a member’s spouse or romantic partner from the shape and density of their network.The authors built some algorithms and do so successfully.

To aid in their model, they invent the concept of network dispersion to characterize your friend network. Their measure of dispersion isn’t what you might initially assume: the more the better. Put another way, the more diverse your friend collection is between you and your spouse, the more powerful a bond is between the two of you and the more likely it is your marriage (or relationship) will last longer. The two authors also did time-series analysis, looking at how your friend networks change and relate that to your changing relationship status that you post publicly to Facebook.

Another interesting result from the paper is that the researchers used two different datasets: one was a subset of the other and focused on larger and denser friend networks. Both sets used randomized and anonymous data from across a large swatch of Facebook members. The results were very similar, showing diversity doesn’t matter how big your network is.

It is also heartening to see that people who are “connectors” (as Brad Feld uses the term) play important roles in one’s friend network. We connectors (and I count myself among the group) are the ones who create the network path diversity, and help to stitch together the smaller sub-groups that boost the dispersion factor. This makes sense to me.

There are many other efforts involved in mapping relationships, including one that Dean Collins developed one many years ago but it is no longer available.

One that you can access quickly and free is LinkedIn Inmaps here. When I first heard about this program several years ago I was fascinated with my own map, but sadly, they have tuned the software to only look at smaller networks than mine. Perhaps your account will be able to work with their software.

So there you have it: not only do opposites attract, but they stay attracted longer. If you have any links to other relationship mapping or visualizations, share them here in the comments.