I will present an algebraic approach to stochastic graph-rewriting. Rules are seen as particular elements of an algebra of “diagrams”: the diagram algebra D. Diagrams can be thought of as formal computational traces represented in partial time. They can be evaluated to normal diagrams (each corresponding to a rule) and generate an associative unital non-commutative algebra of rules: the rule algebra R. Evaluation becomes a morphism of unital associative algebras which maps general diagrams in D to normal ones in R. In this algebraic reformulation, usual distinctions between graph observables (real-valued maps on the set of graphs defined by counting subgraphs) and rules disappear. Actual graph-rewriting is recovered as a canonical representation of the rule algebra as linear operators over the vector space generated by (isomorphism classes of) finite graphs. This shift of point of view, away from its canonical representation to the rule algebra itself, has unexpected consequences. We find that natural variants of the evaluation morphism map give rise to concepts of graph transformations hitherto not considered. This is joint work with N. Behr and V. Danos.