For highly configurable software systems, such as the Linux kernel, maintaining and evolving variability information along changes to source code poses a major challenge. While source code itself may be edited, also feature-to-code mappings may be introduced, removed, or changed. In practice, such edits are often conducted ad-hoc and without proper documentation. To support the maintenance and evolution of variability, it is desirable to understand the impact of each edit on the variability. We propose the first complete and unambiguous classification of edits to variability in source code by means of a catalog of edit classes. This catalog is based on a scheme that can be used to build classifications that are complete and unambiguous by construction. To this end, we introduce a complete and sound model for edits to variability. In about 21.5ms per commit, we validate the correctness and suitability of our classification by classifying each edit in 1.7 million commits in the change histories of 44 open-source software systems automatically. We are able to classify all edits with syntactically correct feature-to-code mappings and find that all our edit classes occur in practice.