\textit{J. C. Raoult} [ibid. 32, 1-24 (1984; Zbl 0551.68065)] has given a description of graph rewriting. His description is operational, despite the similarity which his constructions have to the category-theoretic concept of a pushout. We describe a modification to Raoult's description of graph rewriting which allows the reduction of a redex to be described as a pushout, in a category of graphs where morphisms are not required to preserve graph structure. Our description can also handle term rewrite rules whose right-hand sides consist of a variable. Raoult specifically excludes such rules from his treatment. Rules of this form include the K combinator, the identity function, selector functions fors model sheds light on why some instances of NP-complete problems are solvable in practice with a low average complexity.