this kind of thing might be interesting for local search algorithms where you want to explore different variations / adjustments of a particular structure and w

this kind of thing might be interesting for local search algorithms where you want to explore different variations / adjustments of a particular structure and want to maintain some kind of topological invariants while you are doing so. E.g. search the neighbourhood of a given tree by adding / deleting edges, while preserving that what you get is in fact still a tree