<p>Multiplayer quantum games have received growing attention due to the ability of quantum computational models to access enlarged strategic spaces, thereby enabling the emergence of nonclassical Nash equilibria and Pareto-efficient solutions. Concurrently, graph-theoretic representations have become a standard tool for encoding relational dependencies among interacting players. This work establishes a unified formalism that embeds arbitrary graph topologies into parametrized quantum-game circuits, providing a direct mapping between network structure and the strategic interaction space of quantum players. Within this framework, we analytically and computationally evaluate how graph-induced interpersonal couplings modulate payoff distributions over repeated quantum-game iterations. In addition, we integrate a reward-driven adaptation algorithm that allows players to optimize their local strategy parameters dynamically with respect to accumulated payoffs. Experimental results demonstrate that the equilibrium reward landscape is highly sensitive to the players’ graph-theoretic centrality and the weighted structure of their adversarial and cooperative relationships.</p>