Union-find
Also known as: Disjoint-set, DSU, Merge-find set
Union-find (disjoint-set union, DSU) maintains a partition of elements under two operations: find (which set is this in?) and union (merge two sets). Path compression plus union-by-rank gives nearly $O(1)$ amortized time per op (inverse Ackermann).
Kruskal’s MST, connected-component maintenance, and “are these two nodes already linked?” queries are the standard uses. It is a graph connectivity tool without building full adjacency structures for every query mix.