Today I showed a bunch of examples of other complex networks besides the web and illustrated that the properties we saw in the web graph aren't special to the web -- they happen in most of these other networks too. So, they are in some sense "universal".

This motivates two natural directions:

1) Trying to understand what causes these properties to emerge

2) Figuring out how to exploit these properties.

We'll to 1 and then 2, spending about 3-4 lectures on each.

We started on 1 today by exploring Erdos-Renyi random graphs. What we saw is that through a very simple random graph model we could obtain connectivity structure (a giant component and a small diameter) that very closely mimic what we saw in the web graph and the other networks. So, in some sense, there is a very simple explanation of these properties -- they result from independent random connections.

But, the Erdos-Renyi graph does not provide an explanation for clustering or heavy-tailed degree distributions. Understanding why these occur so often will be the focus of the next two lectures.

## Monday, January 10, 2011

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