Ground-based radar networks are the primary sensor infrastructure for space situational awareness, supporting continuous orbit determination and catalogue maintenance across the growing low-Earth-orbit population. As network deployments become geographically denser, independent scheduling policies produce redundant simultaneous observations of well-tracked objects while leaving others near their uncertainty thresholds without timely coverage. This paper proposes graph-enhanced multi-agent reinforcement learning (GM-MARL), a cooperative multi-radar scheduling framework in which a bipartite graph neural network encodes the time-varying visibility structure of the sensor network, enabling each radar to condition its scheduling decisions on the current tracking state of the full target catalogue under the centralised-training decentralised-execution paradigm. A pre-training coupling-metrics protocol is introduced to characterise network coordination demand from radar geometry under a specified target ensemble and episode horizon, providing useful pre-training diagnostic guidance for algorithm selection without requiring trial evaluations. The reward formulation incorporates an urgency weighting that prioritises observations on targets approaching or exceeding the maintenance threshold, combined with a redundancy penalty that discourages simultaneous co-observation of the same target. Evaluation across two network geometries of contrasting coordination demand shows that GM-MARL matches the best observed terminal maintenance rate in the zero-coupling global configuration while remaining within 0.5 percentage points of Greedy on the time-averaged metric. In the high-coupling regional deployment, GM-MARL matches the best observed catalogue-level maintenance performance while increasing the same-step co-observation-free rate from 46.6% to 51.3% relative to independent greedy scheduling, without degrading catalogue maintenance.