Emerging 6G and edge-intelligent networks require effective and balanced routing algorithms among varied and spatially distributed devices. Existing federated routing systems often prioritize aggregate latency or throughput above fairness and the underlying geometric structure of network topologies. This paper describes Geo-FairFed, a geometric fairness-aware routing system that blends hyperbolic graph neural networks (HGNNs) and federated optimization to provide equal performance across edge nodes. Each node learns topology-aware representations on a negatively curved manifold, which include hierarchical relationships and connection asymmetries. A global aggregator next enforces fairness using a curvature-regularized aim that minimizes routing loss, geometric inconsistency, and an inequality penalty based on Jain's fairness index. A theoretical analysis develops convergence guarantees under limited curvature and shows that the proposed fairness term results in a Pareto-improving equilibrium in routing performance. Extensive simulations on dynamic 6G-edge and IoT topologies reveal that Geo-FairFed minimizes average latency by 20\%, reduces energy consumption by 17\%, and improves fairness by up to 21\% when compared to state-of-the-art federated and geometric routing protocols. The study found that embedding topology in a hyperbolic manifold and including fairness into federated updates can significantly enhance the efficiency and equity of large-scale network routing.

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