Recommended – link below.
1. The most basic [type of connectedness] that we all think of is just popularity: how many people you connect with. And that’s very natural – we count how many friends we have on Facebook or how many followers you have on Twitter. And that gives a some idea of the reach of a person… and can be very powerful in marketing certain kinds of things where you just want to get something out quickly and at a fairly shallow level.
Then once you push a bit deeper … you start thinking about other kinds of ways in which people can be well connected.
2. Another way that is very important is not just having many friends but having well-connected friends. And that leads to a notion that’s … somewhat circular, in the sense that your influence comes from the influence of your friends, and their influence comes from the influence of their friends and so forth. And so you end up with a system. But that begins to bring the network into the picture now, because now I care about not only my direct connections but my indirect connections… probably the best example of where that really came up is in Google’s PageRank… [which] is built off of a similar mathematics to this kind of idea of indirect relationships and influence.
…
3. A third type is one that’s often known as “betweenness” centrality, which looks at how well a person is situated as a connector of other groups that might not otherwise have strong connections to each other. And so there’s a question of, am I a strong intermediary? Am I somebody who’s a… broker? Am I a person who’s bringing information or important opportunities and access from one group to another. So that’s another type of important influence that one can have in terms of their position.
4. And then another is how good I am as a spreader of things… How good am I as a diffuser of information? Can I diffuse information well, is it going to spread through the network well? And that means I have to have some good indirect connections, but it’s not an infinite process – it’s how well connected am I in terms of my friends of friends and friends of friends of friends. And am I well positioned to get information out and have people understand it?
Matthew O. Jackson – On Social and Economic Networks – interview with Michael Garfield on Complexity from the Santa Fe Institute