The increased emphasis on clean energy has accelerated the integration of renewable energy sources into electrical grids, resulting in the rise of peer-to-peer energy trading systems. For optimal power dispatch and management the Energy Internet concept advocates using energy routers. Efficient energy routing algorithms are crucial for successful energy transfer between trading pairs in peer-to-peer energy trading across the complex Energy Internet. This research treats the energy routing problem as a non-convex, non-linear optimization problem using a combination technique of graph theory and non-convex nonlinear programming. It efficiently generates a multi-path solution for a trading pair, minimizing energy transmission loss while considering power flow direction constraints and accurately computing power losses during transmission which has not been considered in existing energy routing algorithms. A semi-decentralized approach with a priority concept is proposed for managing simultaneous power transmissions from multiple energy trading pairs, to avoid congestion and shift computational workloads to individual routers and the network system operator. The approach’s performance is assessed through numerical simulations and comparisons with existing energy routing algorithms to showcase its novelty in power loss reduction, congestion management, and adaptability.