Structural universals have been introduced in the philosophical literature on examples such as chemical molecules composed of bonded atoms of different kinds. They are useful to handle complex abstract entities such as designs of artefacts, shapes, strings, words and texts, relevant in many areas of applied ontology. We use graph-theory as a unifying framework to review and compare the formal accounts proposed by Armstrong, Bennett and Mormann. We then propose a more expressive account, combining features of Bennett's and Mormann's proposals, able to model both the mereology of complex states of affairs and the structure of the particulars involved in them. Structural universals are explicitly represented; their structure, where a same universal can be part of a structural universal several times over, can be read off the graphs representing complex states of affairs.
