
I'm not aware of articles treating graphs as Kleene algebras (I haven't looked for them though). Conway's "Regular Algebra and Finite Machines" [1] and Kozen's "A Completeness Theorem for Kleene Algebras and the Algebra of Regular Events" [2] are interesting texts to read on Kleene algebra.
[1] https://www.amazon.com/Regular-Algebra-Finite-Machines-Mathe...
Conway worked out some results for non-serialised (commutative) events in Regular Algebra and Finite Machines about half a century ago.