Basic graph theory: connectivity, degree distributions, trees, adjacency matrices, spectrum.
Random graphs: Erdos-Renyi, configuration model, preferential attachment, small-world, branching process approximations
Flows and games on graphs: max-flow, min-cut, optimal transport, Wardrop equilibria, evolutionary dynamics.
Random walks on graphs: invariant distributions, hitting times, mixing times.
Dynamical systems on graphs: distributed averaging, interacting particle systems, epidemics, opinion dynamics. Mean-field and branching process approximations.