  Conceptual Graphs (CGs) are a formalism to represent knowledge. However
producing a CG database is complex. To the best of our knowledge, existing
methods do not fully use the expressivity of CGs. It is particularly
troublesome as it is necessary to have CG databases to test and validate
algorithms running on CGs. This paper proposes CG2A, an algorithm to build
synthetic CGs exploiting most of their expressivity. CG2A takes as input
constraints that constitute ontological knowledge including a vocabulary and a
set of CGs with some label variables, called $\gamma$-CGs, as components of the
generated CGs. Extensions also enable the automatic generation of the set of
$\gamma$-CGs and vocabulary to ease the database generation and increase
variability.
