This question is motivated by a issue regarding network motifs. To determine if a (connected, induced) subgraph $H$ occurs with significantly high frequency in an input network $G$, we generate an ensemble of comparison networks similar to $G$ and count the number of occurences of $H$ in them. Thus we obtain the number of copies of $H$ in $G$ (call this frequency $f$), and the number of copies of $H$ in the comparison networks (call these frequencies $x=(x_1,x_2,...,x_n)$).

A trade-off arises: We want $n$ to be large in order to give a better comparison, and $n$ to be small to be able to actually perform the computation. I'm concerned, however, that sometimes $n$ is chosen too small.

Question: How can we determine if $n$ is too small? I.e. how can we determine if we have sufficiently many comparisons?

My feeling is to compare $f$ with the mean of datasets $x$ and c(x,ceiling(mean(x))) [in R notation]. I.e. in the second case, we add an artificial point to the dataset, which is close to the mean of $x$, integral and non-zero. The idea is, if we instead chose to use $n+14 comparison networks, and the new comparison graph turned out to have ceiling(mean(x)) copies of $H$, would we have come to a different conclusion? If so, this would indicate that $n$ is too small.


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