Algorithm 1:

Difference Degree Test

1: Construct difference network $\overline{\mathit{D}}={\left\{{\overline{d}}_{ij}\right\}}_{i,j}$

2: Obtain first and second moments of $\overline{\mathit{D}}$, that is, $\overline{e}=E\left({\overline{d}}_{ij}\right)$ and ${\sigma }^2=\mathrm{Var}\left({\overline{d}}_{ij}\right)$

3: Generate U null Difference Networks, ${\overline{\mathit{C}}}^m(u=1,\dots ,U)$ based on $\overline{e}$ and ${\sigma }^2$

4: Apply the adaptive threshold selection method to find the threshold, γ

5: Apply threshold to $\overline{\mathit{D}}$ to obtain the difference adjacency matrix $\mathbf{A}={\left\{{\overline{a}}_{ij}\right\}}_{i,j}$ and di for node i

6: Generate the null distribution for $d_i~\mathrm{Binomial}\left(N-1,p_i^{\text{null}}\right)$. See Equation (7) for the form of $p_i^{\text{null}}$

7: Assess the statistical significance of the number of DWEs at node i.