Biology is molecules plus mechanisms. Theory allows us to extrapolate mechanisms far beyond the regimes where they were originally observed, but also places bounds on the capabilities of living systems given assumptions about their molecular constituents. We study the logistics system of eukaryotic cells, whose warehouses are micron-scale "organelles" and whose trucks are 10-nanometer-scale "vesicles". Organelles form the nodes and vesicle fluxes form the edges of a transport graph. Unlike traditional logistics systems, this graph is self-organized: vesicles are regulated by the very molecular cargo they carry, and organelle chemical identities arise as a balance of molecular gain and loss. We use rigorous graph theoretic approaches to delineate what kinds of transport graphs are impossible, and large-scale statistical methods to sample what kinds of graphs are likely. Living cells occupy the interesting space between these two boundaries. For this talk, no biology background will be assumed from the audience!