Let's say you're at a big cocktail party. By the end of the evening, who will have spoken with whom? Suppose this is determined completely at random with some fixed probability. That is, for each pair of guests, a die roll determines if the pair has a conversation. This generates a random graph: vertices are guests; edges are conversations. What can we say about the properties of this graph? If one guest brings a juicy rumor, will everyone hear it? In this talk, I'll describe what Erdos and Renyi had to say about this social network, and survey some other mathematical models of social networks.
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