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In general if some terminology exists for an object, the complementary object is called the co-object (assuming it exists).

For the purpose of my research it is very useful to define graphs in reversed order, that is, {(y, x) such that y = f(x)}. I simply referred to them as graphs until now, but the time has come to name them something better! (As much as I would like to, I can't call them "graphs" because they're literally not graphs. I also feel that cograph isn't quite correct although I like the ring of it.)

Thank you

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    How about "antigraphs"? – 2017-02-18
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    How do you define graph? – 2017-02-18
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    Hm I guess antigraph works, but I want to capture the idea of "reflecting" - maybe I'll do some google translating from english to latin haha. As for graphs, they're {(x, y) : y = f(x)}. – 2017-02-18
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    How about what they are normally called, reflections? In particular, these are reflections about the line $y=x$ – 2017-02-18

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I called it a "contragraph" because contra is the usual prefix for reversing something. $\Gamma(f)$ is the usual notation in my field for denoting the graph, so I used \reflectbox{\Gamma}(f) for the contragraph.