Today in class we had our last lecture about network structure. We talked about the combination of high clustering coefficient and small diameter -- so called "small world" graphs. The main take-away is that small-world properties can result from a simple combination of highly correlated local structure combined with random independent long range connections. The example we looked at is a lattice of local connections with added random long range connections.
The second aspect of small world graphs that we focused on is that simple, myopic, distributed agents can actually find the short paths. This turns out to be a much more delicate phenomenon to model. But, we saw that it can be viewed as the result of adjusting the long range connections to be "distance-dependent". However, this dependency on distance has to be very carefully chosen to ensure that myopic agents actually find the short paths.
That's it for network structure! There's a lot more that we could have covered, but for next class we'll move on and discuss "search" ... which will end up making use of some features of network structure.
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