We introduce interactive graph matching, a process that conciliates visualization, interaction and optimization approaches to address the graph matching and graph comparison problems as a whole. Interactive graph matching is based on a multi-layered interaction model and on a visual reification of graph matching functions. We present three case studies and a system named Donatien to demonstrate the interactive graph matching approach. The three case studies involve different datasets: a) subgraphs of a lexical network, b) graph of keywords extracted from the InfoVis contest benchmark, and c) clustered graphs computed from different clustering algorithms for comparison purposes.