Say we have an AF C* algebra $A$ described by some Bratteli diagram $E$. If $M_\infty (A)=\displaystyle{\lim_\rightarrow M_n(A)}$ and $P(A)$ are the projections in this algebra, we know that $K_0(A)^+=P(A)/\sim$ where $\sim$ is the von Neumann equivalence relation, and the Grothendieck group construction gives us $K_0(A)$.

My question is: is there an analogous description of projectors and equivalence at the level of the graph $E$ itself which yields the same $K_0$ group as the AF algebra it describes? I have thought about this question in terms of the path algebra of $E$, but really don't know much about this area.