As a very youthful person in the 1970s, I was delighted to discover support for “my” thesis that relations are prior to things (and much else of interest) in the French writers associated with so-called structuralism. (The Anglophone comparative literature people had not yet invented “poststructuralism”.) There have been many structuralisms and attributions thereof over the years. I tend to be sympathetic to a lot of them — mathematical, linguistic, and historiographical.
From my current perspective, the unifying theme is that structure — of whatever sort —statically captures a field of potential inferences. Fields of potential inference are the basis on which diverse things such as mathematical theories, proprieties of linguistic usage, practices and practical attitudes of individuals, and large cultural formations are all constituted as determinate. I actually use a variant of the notion of static capture in my day job, at the mundane level of capturing potential inferences in a software or data model. (See also Difference; Althusser’s Hegel; Foucault; Empirical-Transcendental Doublet; Archaeology of Knowledge; 1968; Imaginary, Symbolic, Real; Immediacy, Presence; Ricoeur on Structuralism; Genealogy.)
In Aristotelian terms, in addition to structure’s connection with potentiality, what has been called structural causality is actually a good interpretation of efficient causation, and also turns out to look like the operation of an unmoved mover. (See also Structure, Potentiality; Efficient Cause, Again; Potentiality, Actuality; Values, Causality.)