We discuss polariton graphs as a new platform for simulating the classical XY and Kuramoto models. Polariton condensates can be imprinted into any two-dimensional graph by spatial modulation of the pumping laser. Polariton simulators have the potential to reach the global minimum of the XY Hamiltonian in a bottom-up approach by gradually increasing excitation density to threshold or to study large scale synchronization phenomena and dynamical phase transitions when operating above the threshold. We consider the modelling of polariton graphs using the complex Ginzburg–Landau model and derive analytical solutions for a single condensate, the XY model, two-mode model and the Kuramoto model establishing the relationships between them.