Modeling Roommate Dynamics as Social Power Networks
Modeling Roommate Dynamics as Social Power Networks
Continuing with the roommate theme from my last post, every social circle has its quirks. Ideally, everyone in a close knit group of friends or roommates has a strong relationship with everyone else, but in reality most social groups are lopsided, poorly connected, and full of unequal relationships. A power network model can be used to visualize and analyze such things in an interesting if not foolproof way. Consider a house with six occupants, and a ‘relationship’ network something like the following:
As you can see, it’s far from balanced. Although everyone knows each other, the lines show close friendships. F is the center of the group, the guy everyone knew first. A, C, and E are friends, perhaps through a shared hobby, and perhaps all met F together. D, E, and F are close as well, while B is just one of F’s old friends who tags along and doesn’t really share any interests with the rest of the group.
Despite this being completely hypothetical, I’m sure you can find parallels in your own social circles. No group is a perfectly cohesive mess of shared friendships and interests. A social graph like this allows us to instantly and intuitively understand some key dynamics of the group, though. It’s immediately obvious that F is the most ‘powerful’ person in the group; any planned outing that doesn’t include them is going to be tense for someone. Any real interaction between B and the rest of the group has to go through F; to a lesser extent, D is similarly isolated. This are several ways F has power in the group. The power to fully exclude B is the most obvious; B is truly dependent on F, with D being close to it. In much the same fashion, E is the second most powerful, as paths between the ACE block and D exist through them as well.
You can also see that A, C, and E form a bit of a power bloc together – they’re very strongly connected, and represent half of the group. In fact, A and C have identical connections, and are identically ‘powerful’ or ‘valuable’. This self contained bloc can do just fine without F most of the time.
In a hyper limited sense, conversations can act as value exchanges. If you can only talk to one person at a time, you want to choose who will be the most interesting to talk to. Thus, we can assign a value to each node for each edge they have, with the ‘value’ each provides being how interesting the other person will find a conversation with them. Of course, in real life, there are millions of outside influences on this – sometimes you need to tell your roommate to do the dishes regardless of how boring they are – but for a simplistic model, it’s valid enough. Applying this model to the network above, a few conclusions are obvious.
A and C will always have each other, due to their identical connections. F has their pick, making them a market decider. B and D will either become very interesting, or very lonely. If B doesn’t want to talk to F, that’s fine; F is still tied with E for most connected person. But if F thinks someone else has better conversational skills, B will become totally isolated. Also, if something removes the big power bloc, like an event for the hobby they share, things become very awkward very quickly for B and D, especially if F leaves with them.
Of course, another layer to think about is pathing, or how people in the group communicate across multiple ‘nodes’. Let’s say A says something that D takes offense to. A and D aren’t good friends, so D probably won’t talk to them directly about something personal; instead, D will have to complain to F or E about it, pathing the concern through them. Lord help F if B gets upset about something, of offends someone else. In real life, the ‘power’ that F has by virtue of centrality and ‘betweenness’ can be a burden as well. If B is a neat freak, F is going to go crazy relaying this concern to everyone else – or B will go crazy at having it completely ignored.