TADM2E 6.7

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Part A

Probably yes. Using Kruskal's algorithm, you'll still get the same insertion order of edges, regardless of how much you add or subtract from the edge weighting.

Part B

No. Example would be the following graph:

A -1 B
B -1 C
A -1 C

Shortest path from A to C is A->B->C.

If we increase all weights by two, shortest path will change to A->C