It's A Small World (network) After All

Certain ideas have a way of showing up wherever you look. The Golden Ratio appears again and again in art and nature. Chaos Theory becomes integral in just about any interesting real world process. It seems like every time I hear about small-world networks, it's in a new context. You've probably heard of it as well, at least in terms of Kevin Bacon.

Small-world ends up being an apt description of this phenomena in two ways. First, any two members of the network are "close", in that just a few connections link them. Hence the game Six Degrees of Kevin Bacon, where in fact 4 degrees are unusually distant (an interesting tidbit from the Wikipedia page: Kevin Bacon doesn't make the top 100 list of most central actors. The top billing shifts as new movies are made, but at the time of this posts is held by Dennis Hopper).

Small-world networks also have "clusters", where individual nodes tend to form groups that are more likely to connect internally than externally. Certain directors regularly use the same actors. An even more clear example is your own social network: you're probably a member of a couple friend groups, where everybody knows everybody else. Hence the entire world is small (compact), but it's also made up of lots of small worlds (clusters).

Why do small world networks matter? We're not exactly sure. There are theories that it's because they're more robust to damage (dropped nodes or edges). Alternatively, it could be that the rules that lead to them (e.g., preferential connection to already large nodes) are common, unrelated to any desirable network property. But although the reason is up for debate, they show up so often something must be up. The interactions between your genes, some ecological systems, brain structure, rock fractures, and social networks are all small world networks. As graph theory spreads through more fields of science I suspect many more examples will be found.

I'm sure I'll post about small networks again, as their tendency to pop up everywhere makes them a good tool for understanding the connections between disparate fields, but I'd like to use them in this post to talk about jobs. I don't have any empirical evidence this is so, but I suspect people's ability to take a job forms a small world network. There are definitely hubs: lots of people are qualified to work at Wal-Mart. There are certainly clusters: Aerospace Engineers could replace each other, but not many other people could. Is the network compact? That's precisely my concern, it appears to be spreading out. If nature finds small world networks to be so important, is that safe?

Let's assume some salesmen know a field really well, and some can just pitch anything. Let's assume the ones who know that field really well could move into some other aspect of it, like management. Let's consider a world where the car industry is declining, and robotics is really catching on. The competition for the sales jobs in the car industry is going to increase, and commissions will be shrinking. Meanwhile, the growing robotics field is likely in need of more workers, so salaries will be comparatively high. Those deeply enmeshed in the automotive world are stuck, but the universal salesmen will move on to greener pastures. As salesmen flow into robotics, the situations are likely to stabilize, and now that the demand is met, salaries will start declining again. Since managing a robotics plant might not be as transferable a skill as sales, that aspect of the field will still be in demand: the sales guys who know robotics well will have the opportunity to move into management. Thus there's a net flow from car sales into robot plant management, even though none of the car salesmen were qualified for that position. A small world network means that indirect actions can still be very powerful. If 10 people needed to each switch jobs to transfer personnel from one field to another, the mechanism would be far too slow and weak to be meaningful.

When everyone was farmers, the only limits for job replacement were geographic in nature. As occupations require greater and greater skill and training, we appear to be breaking into clusters. The highly educated can move within a couple fields, although not universally. Additionally, these fields may be clustered, so aerospace and pharmacology might be high skill but weakly linked. Meanwhile, large portions of the population lack the education for any of these technically challenging fields, and so are stuck in there own cluster. As certain fields declining (see, e.g. Detroit), there isn't the same opportunity to move that labor indirectly to cutting edge fields like nanotechnology: the path from assembly line worker to materials scientist is too long and one directional. You'd expect, then, the very universal hubs of entry level positions would get inundated, as that's the common direction from all the declining industry. The competition between the young and old for jobs suggests that's exactly what's happening right now.

Could the recession be partially our economy diverging from small world principals? It's something I lack evidence for, but that's worth considering. The economy may be becoming resistant to change at the same time the uncertainty about the future is growing. It's an interesting thought as well, because it suggests that this is something we could measure and take specific actions to address. Some fields are inherently high-skill, but some can be achieved by either. Farming is increasingly done by small groups of scientists. They're more likely to be able to switch to other important fields, and farming can clearly be done as a human labor intensive activity, so a transformation towards smaller farms might help keep the system more compact (and farming has arguably held this role since civilization form). It also suggests that opportunities for workers to get new training, and broad, cross-discipline degrees would help. The auto industry probably become a bigger hub as other manufacturing industries closed their doors: if we'd seen that more and more people were concentrating in a single industry we could tried to promote new links between it and other fields, or otherwise prepared for the coming problems. I'm interested to see how network gets applied to this and other problems, as it has the potential to help us understand underlying problems before they surface or at least to connect symptoms to a cause.