We present the analytical solution of the mean-field Hubbard model of undoped and doped graphene rectangulenes. These are nonchiral graphene rectangles of arbitrary length and width, and nanoribbons are thus narrow rectangulenes. We rewrite the Hubbard model on the basis of exact bulk and edge noninteracting eigenstates, and we provide analytical expressions for the Coulomb integrals. We also present a general mean-field decoupling of the Hamiltonian that is valid at any temperature and doping. We introduce the edge-only doping regime and discuss the paramagnetic, ferromagnetic, and antiferromagnetic mean-field solutions in this regime. We calculate explicitly at zero temperature the eigenenergies, occupations, spin densities, and the addition energies of rectangulenes with lengths and widths ranging from a nanometer to several hundreds of them. We rewrite the exact mean-field tight-binding Hamiltonian back in the site-occupation basis.

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• Edge states
• Magnetic order
• Graphene
• Hubbard model