Interdependence between gas and electricity transmission networks is a subject of concern due to the expanding use of gas for electricity generation in combined-cycle power plants around the world. This paper proposes a novel and much more accurate representation of natural gas and electrical networks based on graph theory, which includes all the assets of both systems and their couplings and offers a more realistic topological model of the two coupled networks. The representation is proposed as a scale-free graph and is mathematically validated in test networks, finding that the representations maintain the same characteristics of traditional graphs, but with more topological detail of the infrastructures.