An heavyweight ontology is a lightweight ontology (i.e. an ontology simply based on a hierarchy of concepts and a hierarchy of relations) enriched with axioms used to fix the semantic interpretation of concepts and relations Such an ontology can be a domain ontology, an ontology of representation, an ontology of PSM, etc In our work, we argue in favor of using a graph-based solution to deal with the different activities related to Heavyweight Ontology Engineering, in particular ontology representation, ontology operationalisation, ontology evaluation (i.e. verification and validation) and ontology matching Our approach consists in using the graph-based paradigm to represent all the components of an heavyweight ontology (i.e. Concepts, Relations and Axioms) and using graph homomorphism techniques to compare (at the conceptual level) the core components of an heavyweight ontology: the Axioms This explicit graph-based representation of axioms coupled with reasoning capabilities based on graphs homomorphism facilitates both (1) the definition of important notions for Heavyweight Ontology Engineering such as Compatible/Incompatible Axioms or Specialisation/Generalisation of Axioms and (2) the topological comparison of axioms, which in our work is used to define a new approach of ontology matching mainly based on axiom-based ontology morphisms.