By integrating in the representation of electrical circuits the properties of the physical laws which govern their functioning, we propose away to construct a representation such that two circuits which “function in the same way” have the same representation. In this article, we show that the bond graph representation is a good candidate for such a functional representation because its formalism deletes a piece of information which is useless for analyzing the circuit's functioning. But the existing algorithms which transform a circuit into a bond graph are not fully adapted to this formalism. A more suitable algorithm is proposed, based on the 'htte decomposition of graphs. This algorithm associates a unique bond graph with a given circuit and it formalizes the “inspection method” suggested by Karnopp. With this new algorithm, the gap between the bond graph representation and the functional representation is reduced.