<p>We study quantum and classical correlations in the Fermi-Hubbard model on a graphene honeycomb lattice, analyzing the effects of nearest-neighbor and on-site Coulomb interactions, as well as temperature, on entanglement (EOF), classical correlations, total correlations, and quantum discord. Our results demonstrate that both nearest-neighbor and on-site Coulomb interactions play a critical role in enhancing and maintaining quantum correlations. The analysis reveals that weaker or stronger values of Coulomb interactions will lead to a reduction in quantum and classical correlations. Furthermore, our findings indicate that both the EOF and quantum discord exhibit strong sensitivity to temperature variations, whereas classical correlation shows an increasing trend under the same thermal conditions. Finally, we have shown that classical correlation always exceeds quantum discord, but EOF may surpass or fall below both correlations. By optimizing the nearest-neighbor and on-site Coulomb interactions, we can mitigate the detrimental effects of temperature, resulting in enhanced classical and quantum correlations. These findings offer insights into controlling quantum resources and strategies for quantum physics and its practical applications in quantum information processing.</p>