title: Can two Minimum Spanning Trees for the same graph have different edge weights?
body: <p>A graph can have many different Minimum Spanning Trees (MSTs), but can different MSTs have different sets of edge weights? For example, if an MST uses edge weights {2,3,4,5}, must every other MST have edge weights {2,3,4,5}, or can some other MST use a different collection of weights?</p>
  
  <p>What gave me the idea is property that a graph has no unique MST only if its edge weights are different.</p>