How to deduce gene coexpression network is worth thinking.

I read the paper named "High dimensional co-expression networks enable discovery of transcriptomic drivers in complex biological systems" which focus on gene co-expression networks.

the signed correlation：

\(a_{i, j}=\frac{1+\operatorname{cor}\left(x_i, x_j\right)}{2}\)

In order to emphasize strong correlations, we raise the elements of A to a power β, and we refer to this as soft power thresholding.

\(\begin{array}{r}\alpha_{i, j}=\left(a_{i, j}\right)^\beta \\ \tilde{\alpha}_{i, j}=\alpha_{i, j} \times \operatorname{sign}\left(\operatorname{cor}\left(x_i, x_j\right)\right)\end{array}\)

Now we have the gene-gene correlation raised to a power β, and an alternative metric ̃ αi,j which also retains the sign of the correlation between these genes. The final co-expression network is then computed as a signed topological overlap matrix (TOM). The TOM describes shared neighbors between the a pair of genes (i, j). We define the signed TOM as

\(\operatorname{TOM}_{i, j}^{\text {signed }}=\frac{\left|\alpha_{i, j}+\sum_{u \neq i, j} \tilde{\alpha}_{i, u} \tilde{\alpha}_{u, j}\right|}{\min \left(k_i, k_j\right)+1-\left|\alpha_{i, j}\right|}\)

Reference