Distributed reward systems circulate digital value through points, referral bonuses, coupon credits, vouchers, cashback balances, and partner-linked entitlements. Coordinated fraud in such systems often spreads across multiple accounts and shared infrastructure, weakening account-level screening. This article examines how graph theory can support the detection of collusive fraud rings in reward platforms with distributed value flows. The study draws on ten recent publications on graph anomaly detection, graph fraud detection, dynamic graphs, hypergraph learning, frequency-aware modeling, and interpretable graph analytics. The analytical section identifies the structural signatures of collusion, clarifies which graph representations expose them most effectively, and formulates a deployment model for ring-oriented detection. The article argues that collusive abuse becomes more legible when accounts, devices, addresses, payment instruments, referral links, and redemption paths are modeled as one evolving multi-entity graph. The proposed synthesis offers a practical basis for scoring, analyst review, and enforcement design in reward ecosystems.