  We consider the Ising model for two interacting groups of spins embedded in
an Erd\"{o}s-R\'{e}nyi random graph. The critical properties of the system are
investigated by means of extensive Monte Carlo simulations. Our results
evidence the existence of a phase transition at a value of the inter-groups
interaction coupling $J_{12}^C$ which depends algebraically on the dilution of
the graph and on the relative width of the two populations, as explained by
means of scaling arguments. We also measure the critical exponents, which are
consistent with those of the Curie-Weiss model, hence suggesting a wide
robustness of the universality class.
