We expand on some invariants used for classifying nonselfadjoint operator algebras. Specifically to nonselfadjoint operator algebras for which there is a homomorphism (which is also a conditional expectation) onto a commutative diagonal we construct an edge-colored directed graph which can be used as an operator algebra invariant.
"Graph theoretic invariants for operator algebras associated to topological dynamics." Rocky Mountain J. Math. 46 (1) 131 - 146, 2016. https://doi.org/10.1216/RMJ-2016-46-1-131