Yes! Graphs have many interesting algebraic properties.
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.
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...
[2] https://www.cs.cornell.edu/~kozen/papers/ka.pdf