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Is the image provided for a Cayley Diagram of $D_{4}$ in Wikimedia Commons wrong?

The image there seems to have the "outer ring" flipped:

enter image description here

Shouldn't this look more like this:

enter image description here

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    @raxacoricofallapatorius: Not that I am aware of; there really is no essential problem attached to this issue, since any argument that uses one convention can be done, *mutatis mutandis*, using the other convention. I think the article on Cayley graphs is$a$bit of$a$problem because it uses one definition and then has an example using the other convention, but I haven't taken the time to bring it up in the talk page (perhaps you can).2012-05-19

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In the Wikipedia diagram, the red arrow corresponds to multipication by $a$ on the left; your diagram is making it correspond to multiplication by $a$ on the right. Both conventions are okay, but it is true that the convention of the diagram clashes with the convention of the text.

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    Adapted from comments above.2012-09-06