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The Momentum of Social Networks (Part 5): Barycenters

Written by: Bill Sherman on Monday, 18 August 2008, 6:40 AM

Last week, I explored the concept of momentum within relationships. It’s not just whether you have a strong or weak tie, it’s also the momentum (strengthening or weakening). We discussed radial vectors and Doppler shift.

Social network analysis often captures a “moment in time” and assumes that relationships are static, but we all know from experience that they’re highly fluid and constantly changing.

The Doppler shift (approaching and receding) provides a foundation for today’s discussion where we’re going to talk about orbital mechanics, two-body problems, and barycenters. (Did I mention that as a child I wanted to be an astrophysicist?)

When do “weak ties” and casual acquaintances become “strong ties”? When we have weak ties, I may be aware of your goals and help, but I do not view them with the same weight as my goals. The stronger the connection, the more I’m likely to give your goals the same weight as mine. Increasingly, in a strong relationship pair (personal or professional), your needs become my needs. Your obligations become my obligations.

Surprisingly, there’s a very nice way to visualize momentum within networks. In orbital mechanics, objects orbit around a common gravitational center. Let me explain through a picture.

In this purely circular orbit, the two remain equidistant and balanced around a common center. If I were standing on either node, I wouldn’t notice the distance increasing or decreasing.  You can look at this very much like a balanced relationship (which could either be a strong tie or a weak tie (which would depend on the distance from the barycenter).

Now, let’s look at a different case in orbital mechanics (where the two bodies are of different sizes). Let’s call the larger one the earth and the other the moon.

If watch closely, you’ll see that the larger body (the earth) wobbles slightly–because it’s puled by the smaller body (the moon in this case). This visualization is relevant because not every social network pair contains two people with equal amounts of power, wealth, or fame. This graph could represent a boss and subordinate.

You could also look at the earth-moon image as a representation of an individual’s influence on a group–the group tugs the individual and the individual tugs the group (proportionate to their relative size and mutual center of gravity).

We’ve been looking at two-body problems, but our social networks contain far more than us and someone else (ego and alter). Everyone within our network exerts a pull on us, and we exert a pull ono everyone within our network. Even weak ties exert an influence.

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