Can We Decouple Opportunity Through Algorithmic Redistricting? A Graph-Based Approach to School Desegregation

School attendance boundaries are the primary mechanism assigning students to public schools in the United States, yet they also institutionalize inequalities by tying educational access to residential location. This study develops a computational framework that models school segregation as an emergent property of an urban school choice network. Using census block-group and elementary school data from Chicago, I construct a heterogeneous graph encoding community-school utility, inter-school competition, and geographic adjacency, and train a Graph Neural Network (GNN) to predict school-level integration measured by normalized Shannon entropy. The model achieves consistent accuracy across three preference specifications governing the quality-distance tradeoff (MAE=0.078-0.086), and feature importance analysis reveals that school-school competition edge weights are the most influential predictors of integration outcomes. I then simulate two counterfactual boundary interventions: MCMC-based redistricting, which directly redraws attendance zones, and pairwise opportunity merging, which expands enrollment options by joining adjacent districts. Redistricting shifts integration at the extremes of the distribution but does not meaningfully raise the center, while opportunity merging produces more consistent systemic improvements - reducing the share of students in low-integration schools and compressing inequality across the system - with nearly all gains materializing at low participation rates. Together, these findings point to a form of structural inertia: even when boundaries are redrawn, the underlying competitive structure among schools and the residential sorting patterns that shape community demographics remain largely intact, constraining what boundary reform alone can achieve in the short run.