On the exact computation of the graph edit distance

•We consolidate the state on the exact computation of GED by presenting all existing algorithms in a unified way.•We harmonise the definitions of GED employed in different research communities.•We provide a speed-up for uniform and a generalisation to non-uniform edit costs of two state of the art algorithms.•We suggest the smallest currently available IP-formulation of the problem of computing GED.•We provide the first empirical evaluation that compares all available algorithms for the exact computation of GED.