  We show how graph theory can be combined with quantum theory to calculate the
electronic structure of large complex systems. The graph formalism is general
and applicable to a broad range of electronic structure methods and materials,
including challenging systems such as biomolecules. The methodology combines
well-controlled accuracy, low computational cost, and natural low-communication
parallelism. This combination addresses substantial shortcomings of linear
scaling electronic structure theory, in particular with respect to
quantum-based molecular dynamics simulations.
