Today we finished up our discussion of the web graph by looking at "clustering" and then we plowed through a discussion of how the 4 properties we saw in the web graph show up in a wide variety of other networks, and so are "universal" in some sense.

From here we're going to try to understand where these properties come from? The idea is that since all these networks (which evolve or are built using very different mechanisms) have the same structural properties, there must be some simple and universal explanation as to where the properties come from.

To try to understand this, we started with the simplest possible idea of how a graph might form -- as a sequence of independent random connections being made. This led us to the Erdos-Renyi random graph, which we started to discuss, and will continue to discuss during the next lecture.

I've posted the notes for lecture 3 "Beyond the web" on the course website already, but I'll hold off on posting the notes for the Erdos-Renyi graph until Wednesday when we finish discussing them.

## Monday, January 11, 2010

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