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Care coordination failures include missed referrals, lost follow-ups, fragmented communication, and incomplete transitions between primary and specialty care. These failures can delay diagnosis, weaken continuity, and increase avoidable utilisation. Existing detection approaches often depend on manual review, retrospective audits, or simple rule-based flags. Such approaches are poorly suited to capture the relational complexity of patient, provider, referral, messaging, and encounter networks. This article develops a conceptual graph-based machine learning model for predicting care coordination failures. The model represents patient–provider referral networks enriched with follow-up status, patient message activity, specialty access delays, and provider communication patterns. The proposed approach uses a heterogeneous graph neural network in which patients and providers are nodes. Referral, encounter, and messaging relationships are represented as edges, while node and edge features encode follow-up adherence, message frequency, wait-time signals, and communication context. Conceptually, the model would identify high-risk referral edges that combine delayed access, incomplete follow-up, weak messaging activity, or limited provider communication. These predictions would support coordinator review before a referral becomes a documented care gap. A graph-based model could shift care coordination from reactive tracking toward predictive prevention. By identifying fragile referral relationships early, it could support more timely outreach and safer continuity of care.