Researchers have adopted deep learning for classical discrete choice analysis as it can capture complex feature relationships and achieve higher predictive performance. However, the existing deep learning approaches cannot explicitly capture the relationship among choice alternatives, which has been a long-lasting focus in classical discrete choice models. To address the gap, this paper introduces Graph Neural Network (GNN) as a novel framework to analyze residential location choice. The GNN-based discrete choice models (GNN-DCMs) offer a structured approach for neural networks to capture dependence among spatial alternatives, while maintaining clear connections to classical random utility theory. Theoretically, we demonstrate that the GNN-DCMs incorporate the nested logit (NL) model and the spatially correlated logit (SCL) model as two specific cases, yielding novel algorithmic interpretation through message passing among alternatives' utilities. Empirically, the GNN-DCMs outperform benchmark MNL, SCL, and feedforward neural networks in predicting residential location choices among Chicago's 77 community areas. Regarding model interpretation, the GNN-DCMs can capture individual heterogeneity and exhibit spatially-aware substitution patterns. Overall, these results highlight the potential of GNN-DCMs as a unified and expressive framework for synergizing discrete choice modeling and deep learning in the complex spatial choice contexts.