Emerging technological advances in wireless communication and networking have led to the design of large scale networks and small sensor units with minimal power requirements and multifunctional processing. Though energy harvesting technologies are improving, the energy of sensors remains a scarce resource when designing routing protocols between sensor nodes and base station. This paper proposes a multi-hop graph-based approach for an energy-efficient routing (MH-GEER) protocol in wireless sensor networks which aims to distribute energy consumption between clusters at a balanced rate and thus extend networks’ lifespans. MH-GEER deals with node clustering and inter-cluster multi-hop routing selection. The clustering phase is built upon the centralized formation of clusters and the distributed selection of cluster heads similar to that of low-energy adaptive clustering hierarchy (LEACH). The routing phase builds a dynamic multi-hop path between cluster heads and the base station. Our strategy is about exploring the energy levels in the entire network and using these to select the next hop in a probabilistic, intelligent way. Performance evaluation shows that MH-GEER minimizes energy depletion in distant clusters and ensures load balancing in a network, thus improving the network’s lifetime and stability compared with single-hop conventional LEACH protocol.