Protein homodimers pose some intriguing questions about the relation between structure and stability. We approached the problem by means of a topological methodology based on protein contact networks. We correlated local interface descriptors with structure and energy global properties of the systems under analysis. We demonstrated that the graph energy, formerly applied to the analysis of unconjugated hydrocarbons structures, is the bridge between the topological and energetic description of protein complexes. This is a first step for the generation of a "protein structural formula", analogous to the molecular graphs in organic chemistry.