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Two-dimensional (2D) materials have attracted considerable attention for next-generation electronic, optoelectronic, and catalytic applications; however, their performance is strongly influenced by the presence and stability of atomic-scale defects. Defect formation energy plays an essential role in defect prevalence, lattice stability, and functional behavior. Still, its evaluation remains challenging due to the complexity of defect-induced structural perturbations and the limitations of equilibrium-first-principles approaches. This paper presents an entirely conceptual framework that reframes defect formation energy estimation as a graph-structured inference problem. Leveraging graph neural networks (GNNs), the proposed defect-aware graph neural architecture (DAGNA) represents pristine and defect-perturbed lattices as coupled relational graphs, enabling structured propagation of defect-induced information across spatial scales. Instead of proposing a predictive or validated model, the framework explains how hierarchical message passing, defect-aware embeddings, and physics-constrained aggregation can be organized to regulate information flow under defect perturbations in two-dimensional systems. By synthesizing advances in graph theory, the physics of defects, and materials-focused AI, this work provides an operational decision-making framework for reasoning about defect formation energy without relying on empirical datasets or simulations. This framework contributes to the theoretical foundations of applied artificial intelligence in materials science. It provides a clear, physically grounded architecture for future studies in defect-aware materials modeling and defect engineering.