Previously I discussed networks and the notion that we use the word “network” all the time. We don’t fully appreciate all that the word connotes, so that what one person thinks of when you say “network” is quite different to another person’s thought.
I mentioned Euler’s solution to a famous “seven bridges problem”, what would become graph theory, with vertexes and edges. The London Tube map is a diagram of nodes and connections. Some stations are highly connected, acting as hubs between many tube lines, some not as many interchanges, but most are connected to only their previous and next station. Bank; Waterloo; Kings Cross; Hammersmith come to mind. If you change lines on your journey, stations like those look like good interchange opportunities and become quite busy — everyone uses them at once. This usually means that more people choose to use them, demonstrating the “rich get richer” behaviour of many networks, called Preferential Attachment. Highly connected vertexes become even more popular because they are highly connected.
I mentioned Six degrees of Separation, that having a close group of people has disadvantages. A homogenous group of people all interested in the same thing for the same reasons are prone to solving the same problems the same way, making the same mistakes, and processing new information with little variance. They spread ‘interesting’ relevant news rapidly with the effect that everyone in the group soon knows what everyone else in the group knows. This might sound nice and cosy and cohesive, but wait. What if one of the group leaves their job?
Some connections between nodes, in other words, some edges between vertexes, are asymmetrical. In other words, they only go one way, and don’t go back. In effect, they are arrows that only point one way. There may be a way back, via a different edge. Or there may not. In such cases, the network becomes a directed network. The food chain is a directed graph, wolves and rabbits are connected. A wolf often eats a rabbit but a rabbit never eats a wolf. A rabbit eats lettuce but lettuce never eats a rabbit. Think of your own personal social networks. Chances are many connections have directed behaviour too. When job hunting, it feels different asking for a reference from your boss than a friend or coworker, the result may be different too. The directed network has an effect on the shape of the network and the timing and flow of information into it and out of it (if any flows out).
It wouldn’t be a surprise to say that a lot of people got their job not because of a cold application in response to a job ad, but because they knew someone, or knew someone who knew someone. When faced with job-hunting again, people will often reach out to those in their immediate networks for any information that might help (as if they were withholding info until just now). People in our own networks know and share the same information and are interested in the same kind of thing, noticing the same kind of opportunities as each other. Widening the range of contacts to people in the network much further away in terms of degrees of connection may actually give better results.
Those distant connections are exposed to other networks that your colleagues might not be, carrying other news not available within your immediate network. Mark Granovetter wrote in 1973 on the “strength of weak ties”. You may find a certain type of person at the periphery of networks, not afraid to cross over into other departments or groups of disciplines. The type of person not willing to pigeonhole themselves and interested in many and various endeavours in life, with contacts across them all. This can be of value — the chance to import knowledge or methods from distant departments. This type of person incidentally is often a catalyst where disruptive innovation can occur, crossing techniques and methods from one discipline they’re exposed to, to another. Even within our own organisations, departments elsewhere in the same company have different and valuable knowledge. If only they were connected. This is the notion of social capital.
In 1967, Stanley Milgram carried out an experiment forwarding letters to strangers to gain more information on the “small worlds property” of some networks. Even at that recent point, debate arose over how many degrees of separation existed in typical real-world networks that we are all familiar with. Exactly how connected was our world? Would two random people in a population know each other? Directly? Through an acquaintance? Through more links than that? The experiment at Harvard was designed to find the average path length between two nodes in the network, in this case, nodes being people. Random people in chosen cities in America were sent a letter to forward to someone in particular, if they knew them, and if they didn’t know them, to send it to someone else they imagined might know the intended recipient. There’s a lot more to the experiment than that, of course, the package introduced the experiment and had postage paid replies to invite participation; tracking postcards back to Harvard, etc, but essentially that’s what the experiment did.
The results were quite interesting and somewhat revealing. In one part of the experiment, 160 letters went out and 24 hit the target, sent to his home address, but 16 of those 24 all came through the same person, a clothing merchant identified as “Mr Jacobs”. Others of the letters came to the target through his office, and over half of these came directly through two other men. Why so many coming in through so few? Are these people acting like the busy stations on the London Underground? Are those men each playing the part of a kind of social hub? This is quite possible. Some people are highly connected, and their highly connected nature increases their connectivity as people favour connecting to the already highly connected — again, Preferential Attachment (the “rich get richer” mechanism), except we’re not necessarily talking about financial riches, but richness of social capital in their social networks.
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