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This is by no means the only algorithm for finding a spanning tree. You could have started with the empty graph and added edges that belong to \(G\) as long as adding them would not create a cycle. You have some choices as to which edges you add first: you could always add an edge adjacent to edges you have already added (after the first one, of course), or add them using some other order. Which spanning tree you end up with depends on these choices.