The wiffle-ball-graph data structure is O(n) for insertion, sure (each new ball has to be tied to a bunch of existing balls and finding them is probably O(n) at

The wiffle-ball-graph data structure is O(n) for insertion, sure (each new ball has to be tied to a bunch of existing balls and finding them is probably O(n) at best), so building an n-node wiffle-graph is O(n^2), but shortest path queries on the data structure are O(n) at any time (again because you have to go find the two nodes of interest, then spread them apart by at most n units of distance). You can also sort all the nodes by distance from any given node in O(n) time by holding the chosen wiffle ball and hanging the graph over the edge of an O(n) tall tower.