03/18/2010 05:12 am ET Updated May 25, 2011

How Much Does Your Network Weigh?

"How much does your life weigh?" This is what Ryan Bingham, George Clooney's character in Up in the Air, asks in the motivational talks he gives when he's not flying around the country firing people as a corporate downsizing consultant. He asks us to imagine putting everything we own, from our knickknacks to our home, and everyone we know, from casual acquaintances to significant others, in a backpack on our shoulders. "Make no mistake," Bingham says, "Your relationships are the heaviest components in your life. All those negotiations and arguments and secrets, the compromises. The slower we move, the faster we die." For Bingham, the lightness of being isn't unbearable -- it's something to be cultivated as the thing that makes life tolerable.

In the film, the idea of weighing relationships is presented as a provocative existential question, and it is. It's also a timely one. Time and distance once quietly did the job of pruning our network of relationships, keeping them to a manageable size. In the age of Facebook and LinkedIn, however, relationships re-emerge and follow us around as we move from stage to stage in our lives.

This isn't a bad thing. But it suggests that we start to think more concretely about our relationship networks as they command a bigger piece of our lives. As it happens, asking how much relationships "weigh" isn't as outlandish as it seems. A great deal of the field of social network analysis is focused precisely on the question of how to quantify relationships and the networks they form. For example, while social network theorists don't talk about the weight of a network, they do talk about the density of a network -- to what extent is everyone in the network connected to everyone else. Networks with a high level of density have some interesting properties. For one thing, high density is difficult to maintain as the size of the network increases--the more people that there are to know, the harder it is for everyone to know everyone as the limits of finite time and energy take hold. Dense networks are also very effective at enforcing social norms -- all those connections mean that news (along with approval or disapproval of what's being reported) travels fast. That's one reason why, if you are a member of a dense network, you want to make sure that you're a member of other networks as well. The more networks you are part of, the more opportunity you have to define yourself and the less vulnerable you are to having the group turn against you. On the other hand, dense networks can be a comforting source of trust and affirmation.

The idea of network density is at the root of an exchange Bingham has with his sister, who calls him while Bingham is striding across an airport terminal. "You're awfully isolated the way you live," she chides him. "Isolated? I'm surrounded!" he retorts. Bingham, of course, is just merely counting the number of people he interacts with (what network theorists call "degree centrality") -- the smiling woman at the check-in counter, the fellow travelers he encounters at airport lounges. But he is disregarding not only the tenuousness of his relationship with them but their lack of relationship with each other. Bingham's network may be vast, but it is also flimsy. So it is that the people on LinkedIn who have what looks like large relationship networks actually might not be very well connected at all. In networks as in so many other things, it's quality, not quantity, that counts.

Today, social networking tools give us the ability to track our networks and thus be more aware of them, in the same way that tracking your expenses on Quicken or Mint makes you aware of how you spend your money. Up in the Air reminds us that we should not merely keep track of our relationships but think about the qualities that define what it is that we are keeping track of.