How to derive false positive and false negative from top-k accuracy?
I think your confusion comes from the fact that the false negative of $M$ as you thought it, is not top-$k$ accuracy but perhaps $1$ $-$ top-$k$. Moreover, how do you evaluate the condition if g' in top-$k$ most similarity graphs with g?
In any case, for your case I thought the following.
Let's say that if the model $M$ returns a value $o &gt; o^*$, where $o, o^* \in [0, 1]$ (and $o^*$ is a threshold value decided by a human), then we assume that $g \equiv g'$; $g \neq g'$ otherwise.
Thus, a false negative of $M$ is when $o &lt; o^*$ but in reality, $g \equiv g'$.
A false positive of $M$ instead is when $o &gt; o^*$ but in reality, $g \neq g'$.
Of course your result will depend on what value(s) of $o^*$ you choose, but now it should be more clear what are FN and FP.