To each graph on n vertices, there is a naturally associated subspace of the nxn matrices. There is a long history of finding properties of this subspace that reflect the underlying combinatorial properties of the graph. In classical information theory `confusability graphs' are used to measure the amount of information that various channels can carry. Recently, these two ideas have been combined by researchers in quantum information theory to try to measure the information capacity of subspaces of the nxn matrices. This talk will be an introduction to this circle of ideas.