  We present a low-scaling diagrammatic Monte Carlo approach to molecular
correlation energies. Using combinatorial graph theory to encode many-body
Hugenholtz diagrams, we sample the M{\o}ller-Plesset (MPn) perturbation series,
obtaining accurate correlation energies up to n = 5, with quadratic scaling in
the number of basis functions. Our technique reduces the computational
complexity of the molecular many-fermion correlation problem, opening up the
possibility of low-scaling, accurate stochastic computations for a wide class
of many-body systems described by Hugenholtz diagrams.
