We introduce DOMINO, a light-matter computing platform that uses the amplitudes and phases of coupled condensate networks to identify dominant subnetworks of weighted graphs. The network structure is embedded in a gain-controlled polaritonic (or photonic) oscillator array, and a physically enforced global-intensity constraint drives the dynamics to a steady state in which only the amplitudes belonging to the dominant subnetwork remain nonzero. On the instances we test, this dominant subnetwork is a clique. The same hardware can then be operated in a second mode in which the phases evolve under the XY dynamics and encode the sign of pairwise correlations, including correlations mediated by indirect paths. This use of both amplitude and phase degrees of freedom goes beyond the scope of standard Ising-type optical simulators, which target spin-Hamiltonian ground states. We benchmark DOMINO on structured and random weighted graphs against the commercial solver Gurobi and a quasi-Newton baseline (BFGS) on the Motzkin–Straus objective, and we apply it to a gene-coexpression network of 386 transcription regulators in the K562 cell line, where it recovers a clique enriched in leukemia-related KEGG pathways. The same mapping applies to any weighted network in which edge weights quantify pairwise similarity.