A social network evolves randomly according to a simple reinforcement scheme. At each step in time, each player chooses another player at random. Their interaction is positively reinforced, so that the probability of one player choosing another in the future is proportional to the number of past interactions of the pair. The first part of the talk will give some motivation for this model and illustrate qualitative features, including a puzzle: why do the simulation data appear to contradict the theorem? The next part of the talk will show how to understand this system using "back of the napkin" computations. The last part will deal with the methods for rigorous analysis of such a system.