On page two of this discussion of spanning trees there are two different tree structures shown, one labeled DFS tree starting from a as the root and the other labeled Spanning tree created by DFS. If I were to write this out on paper my spanning tree would have looked more like the former than the latter.
Are these distinguished here for convenience, one to show the tree structure of the algorithm vs one showing how the spanning tree fits within the original graph layout? Is this a standard convention, to show the spanning tree in the same layout as the original graph? Would it be wrong to diagram the spanning tree using the first layout?