  We theoretically explore nonresonantly pumped polaritonic graphene, a system
consisting of a honeycomb lattice of micropillars in the regime of strong
light-matter coupling. We demonstrate that, depending on the parameters of the
structure, such as intensity of the pump and coupling strength between the
pillars, the system shows rich variety of macroscopic ordering, including
analogs of ferromagnetic, antiferromagnetic, and resonant valence bond phases.
Transitions between these phases are associated with dramatic reshaping of the
spectrum of the system connected with spontaneous appearance of topological
order.
