Pseudocode C3 Permutation Test. This algorithm uses the random permutation test with $r$ random permutations for the p-value, requiring ${\displaystyle \mathcal{𝒪}(r{n}^2\log n)}$ for Mgc. In the real-data experiment, we always set $r=10$,$000$. Note that the p-value computation for any other global generalized correlation coefficient follows from the same algorithm by replacing Mgc with the respective test statistic.
Input: A pair of distance matrices ${\displaystyle (A,B)\in {\mathbb{R}}^{n\times n}\times {\mathbb{R}}^{n\times n}}$, the number of permutations $r$, and Mgc statistic $c^{*}$ for the observed data.
Output: The p-value ${\displaystyle pval\in [0,1]}$.
1:	function PermutationTest($A$, $B$, $r$, $c^{*}$)
2:	for $t:=1,\mathrm{\dots },r$ do
3:	${\displaystyle \pi =\mathrm{R}\mathrm{A}\mathrm{N}\mathrm{D}\mathrm{P}\mathrm{E}\mathrm{R}\mathrm{M}(n)}$	generate a random permutation of size $n$
4:	$$\begin{gathered} {\displaystyle c_0^{\ast }[t]=\mathrm{M}\mathrm{G}\mathrm{C}\mathrm{S}\mathrm{A}\mathrm{M}\mathrm{P}\mathrm{L}\mathrm{E}\mathrm{S}\mathrm{T}\mathrm{A}\mathrm{T}(A,B(\pi ,\pi )) \\ } \end{gathered}$$	calculate the permuted Mgc statistic
5:	end for
6:	${\displaystyle pval(c^{\ast })\leftarrow \frac{1}{t}\sum _{t=1}^r\mathit{I}(c^{\ast }\le c_0^{\ast }[t])}$	compute p-value of Mgc
7:	end function