Erdos Renyi Random Graph Theory

We'll review Erdos and Renyi's famous paper "On the Evolution of Random Graphs"
https://static.renyi.hu/~p_erdos/1960-10.pdf

This paper is famous for exploring the properties of random graphs and finding some very interesting emergent phenomena. One of these is that as the number of edges grows in a graph (with fixed nodes), there emerges a "giant component" near a certain critical threshold. "Most of" the graph suddenly becomes connected.

We'll review this result and probably a few others. The paper is long, and we won't intend to cover the whole thing in detail.

We're not experts on the material, and the group is very informal. Our goal is that everyone walks away with a bit deeper understanding of the material and its applications. The format of the group is discussion, and generally we don't have prepared material. I may prepare a few notes to keep the discussion focused, or may simply share the paper and highlight section of interest while discussing the derivations.