Abstract: The classic Cluster Editing problem (also known as Correlation Clustering in machine learning) asks to transform a given graph into a disjoint union of cliques (clusters) by a small number of edge modifications. When applied to vertex-colored graphs (the colors representing subgroups), standard algorithms for Cluster Editing may yield solutions that are biased towards subgroups of data (e.g., demographic groups), measured in the number of modifications incident to the members of the subgroups. We propose a modification fairness constraint which ensures that the number of edits incident to each subgroup is proportional to its size. To start with, we study Modification-Fair Cluster Editing for graphs whose vertices are split into two subgroups. While trivially polynomial-time solvable in the classic setting, we show that the modification-fair variant is NP-hard if one may only insert edges within a subgroup. However, the variant in its most general form remains fixed-parameter tractable with respect to the number of edge edits. We complement these and further theoretical results with an empirical analysis of our model on real-world data where we find that the price of modification-fairness is surprisingly low, that is, optimal modification-fair solutions are larger by typically only a small percentage than optimal "non-fair" solutions.