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A professor in my grad program gave me the impression that random graphs are an interesting and as of yet largely unexplored area of mathematics (feel free to correct this impression if I'm wrong). I've found the Erdos and Renyi papers from the late 50s/early 60s and nabbed a copy of Random Graphs by Bollobas. I was wondering if anyone could recommend references/reading materials regarding the current state of research in this area, something perhaps more recent than these.


Update: I appreciate the responses and plan to read the information linked. To close out the question,I'm going to (semi-arbitrarily) pick the response with more references in it. Thanks everybody!

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I don't know if "largely unexplored" is a fair characterization. A lot of research in percolation theory is closely related. – Qiaochu Yuan Feb 4 '11 at 19:53
Fair enough. I've also grabbed a copy of "Percolation" (Bollobas and Riordan), and mean to get through it as well. I got the impression from this professor that there was a lot of room to grow here; it's funny he didn't mention percolation, since another professor in our department has published a bit in that area. – user4689 Feb 4 '11 at 20:34

2 Answers 2

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I haven't read either of these thoroughly, but they are recent and look interesting.

Random Graph Dynamics by Rick Durrett

Probability on Graphs by Geoffrey Grimmett

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Thanks for the links, I'll add them to the reading list. – user4689 Feb 4 '11 at 20:30

Something like this?

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Thanks for the suggestion, I'll check it out! – user4689 Feb 4 '11 at 20:30

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