Wednesday, January 5, 2011

Lecture 2

The notes and slides for lecture 2 are now up.

We didn't get quite a far as I'd hoped, but we'll finish up the slides next class by looking at the structure of lots of networks other than the web.

The key take-aways from today's lecture are the following 4 interesting properties:

1) Connectivity:  The web has one "giant" connected component and all other connected components are tiny.

2) Diameter: The distance between nodes is quite small (~6 avg. distance between noes in the SCC) and, for at least the beginning decade of the web, grow logarithmically with the size of the graph.

3) Degrees:  The degree distribution is not Normal... Instead it's heavy-tailed.  This means we should expect a few nodes with really "huge" degree and "lots" of nodes with small degree.

4) Clustering:  The web exhibits strong "homophilly", i.e., if A is connected to B and C it is significantly more likely than random for B to be connected to C.

We'll see next time that these four properties are "universal"...and then we'll try to explain why they are so common.

Don't forget to attend Raga's probability refresher on Friday @ 1pm in Annenberg 213!

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