TopoEdge is a topology-grounded, edge-deployable framework for end-to-end software-defined networking (SDN) configuration generation and repair, motivated by the brittleness of configuration artefacts under topology variation and by strict operational constraints on latency, privacy, and on-site execution. TopoEdge represents each target topology as a router-level graph and embeds it using a contrastively trained graph neural network (GNN), enabling nearest-neighbour retrieval of a verified reference configuration paired with an executable Python driver (a Topotest/pytest test script that orchestrates the emulated network and checks protocol assertions). The target topology, retrieved reference topology, and reference driver are assembled into a topology-grounded retrieval-augmented generation context (TopoRAG), which grounds a distributed, execution-centric generate--verify--repair loop coordinated by a central controller and realised by three role-specialised agents: (i) a Planning agent that produces a topology-consistent configuration plan and a per-device skeleton; (ii) a Generation agent that materialises executable configuration artefacts, including device configurations and the driver; and (iii) a Verification agent that runs the FRRouting Topotest/pytest harness, compresses failures into a compact trace, and emits localised patch directives for iterative repair.