Ultra-high-energy photons ($E \geq 10^{17}\,\text{eV}$) are expected as by-products of interactions between ultra-high-energy cosmic rays (UHECRs) and background radiation fields or galactic matter, as well as from decay of super-heavy dark matter. Despite these various production mechanisms, the diffuse photon flux is too low for direct detection. Consequently, photon searches at UHE must rely on large ground-based detector arrays. In this contribution, we present a method for photon-hadron discrimination based on deep learning algorithms applied to detector simulations within the context of the Pierre Auger Observatory. Our method correlates information from the Surface Detector (SD), sensitive to air-shower particles arriving to the ground, and the Underground Muon Detector (UMD), sensitive to muons with energies above $\sim 1\,\text{GeV}$. We chose graph neural networks (GNNs) for their effectiveness in handling the discrimination task, allowing for an easy and flexible correlation of information from the SD and UMD. This approach is particularly suitable for handling the irregular structures found in SD and UMD configurations, where stations may be missing due to technical issues. Using simulations, the performance indicates that the method has strong potential for identifying photons, suffering at most $10^{-4}$ background contamination at 0.5 signal efficiency. Future studies will delve into how much that background contamination can be diminished.