Do Kruskal's and Prim's algorithms yield the same minimum spanning tree?

Question

Assuming the edges are undirected, have unique weight, and no negative paths, do these algorithms produce the same Minimum Spanning Trees?

Answer 1

Found this which states that if all the conditions I mentioned above are met, a graph necessarily has a unique MST. Therefore, in terms of my question, Kruskal's and Prim's algorithms necessarily produce the same result.

Answer 2

If the MST is unique, all algorithms will perforce produce it.

If the MST is not unique, the outputs might differ due to different node processing orders (even two distinct implementations of the same algorithm can), but the total weights will be identical. In this case, the MST is a misnomer.

Answer 3

To add upon Yves Daoust's answer, the following graph

In this graph, we have 3 nodes and 3 edges, each has the same weight. Obviously any 2 edges will form a MST for this graph. However, which two edges are chosen will depend on not only the algorithm, but the implementation of the algorithm. For instance, if I store the nodes in a list, I may visit them in a different order than if I stored the nodes in a set, even if I use the same MST algorithm from that point on.

In fact, if my implementation relies on pointer arithmetic (which some containers in some languages do), I may even pick a different MST each time I run the algorithm!