There should be an option for "other" and there should be an option for "it depends."
Once, while learning how many edges exist in a complete graph Kn, and we worked with the example K4, when I closed my eyes I visualized a dim blue representation of the graph on a black field. Each edge adjacent on a partcular vertex (3 at a time in this case) illuminated a bright, neon blue in an alternating clockwise fashion, all in a span of less than half of a second. In counting the edges I saw the handshaking lemma in action with instances of some edges being lit 2 times in a row.
I hastily muttered: "En-times-en-minus-one-over-two."
I don't remember exactly what my professor was asking me prior to that moment. I did some pondering on the questions I was asked, but it all came together at that one brief instant.
Mostly, I think of scalars.
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