but one of the more interesting ones is one due to two hungarian mathematicians, paul erdos and alfred renyi. so maybe you could explain to us, what does it mean for a network to be random? >> in contrast to the ordered graph, where everybody has the same number of connections and regular geometry, we might think about those edges being there or not being there with some probability. so we might want to start out in the extreme example where we'll think of everybody being connected to everybody else in the network. and we typically call that the complete graph. and how we're going to make it into a random network is we'll go through edge by edge and flip a coin to decide whether that edge stays or goes. and i have a coin with me -- >> math in action. >> so in this case, we're going to let the edges exist with probability 50-50. >> okay. >> why don't you choose an edge? >> all right. i'm going to take the one in the upper corner over there. >> and that's a tails, so we're going to remove that edge. >> so now i'm going to go for something right in the middle, that one. >> and that one's a head