Counterfactuals have been established as a popular explainability technique which leverages a set of minimal edits to alter the prediction of a classifier. When considering conceptual counterfactuals, the edits requested should correspond to salient concepts present in the input data. At the same time, conceptual distances are defined by knowledge graphs, ensuring the optimality of conceptual edits. In this work, we extend previous endeavors on conceptual counterfactuals by introducing \textit{graph edits as counterfactual explanations}: should we represent input data as graphs, which is the shortest graph edit path that results in an alternative classification label as provided by a black-box classifier?