Why does the spatial positioning of vertices not change a graph?

"One important thing to understand about graphs is which aspects of a diagram are relevant. Specifically, the spatial positioning of the vertices doesn’t matter. In Figure 5.2 we drew Muhammad Ali in the mid-upper left, and Sonny Liston in the extreme upper right. But this was an arbitrary choice, and irrelevant. More specifically, this isn’t part of the information the diagram claims to represent. We could have positioned the vertices differently, as in Figure 5.5, and had the same graph. In both diagrams, there are the same vertices, and the same edges between them (check me). Therefore, these are mathematically the same graph.\n\nThis might not seem surprising for the prize fighter graph, but for graphs like the MapQuest graph, which actually represent physical locations, it can seem jarring. In Figure 5.3 we could have drawn Richmond north of Fredericksburg, and Virginia Beach on the far west side of the diagram, and still had the same graph, provided that all the nodes and links were the same. Just remember that the spatial positioning is designed for human convenience, and isn’t part of the mathematical information. It’s similar to how there’s no order to the elements of a set, even though when we specify a set extensionally, we have to list them in some order to avoid writing all the element names on top of each other. On a graph diagram, we have to draw each vertex somewhere, but where we put it is simply aesthetic."