In this paper we propose a methodology suitable for a comprehensive analysis of the global embodied energy flow trough a complex network approach. To this end, we extend the existing literature, providing a multilayer framework based on the environmentally extended input-output analysis. The multilayer structure, with respect to the traditional approach, allows us to unveil the different role of sectors and economies in the system. In order to identify key sectors and economies, we make use of hub and authority scores, by adapting to our framework an extension of the Kleinberg algorithm, called Multi-Dimensional HITS (MD-HITS). A numerical analysis based on multi-region input-output tables shows how the proposed approach provides meaningful insights.