Well, I have read the contents of this blog. As it explains or rather recommends signed network due to two reasons:

First, more often than not, direction does matter: it is important to know where node profiles go up and where they go down, and mixing negatively correlated nodes together necessarily mixes the two directions together. Second, negatively correlated nodes often belong to different categories. For example, in gene expression data, negatively correlated genes tend to come from biologically very different categories.

But there are also sort of disclaimers:

It is true that some pathways or processes involve pairs of genes that are negatively correlated; if there are enough negatively correlated genes, they will form a module on their own and the two modules can then be analyzed together.

and

By and large does not mean always, and there may be applications in which an unsigned network is preferable. In principle there’s also nothing wrong with carrying out both types of analysis, but working with two related yet distinct analyses of the same data may quickly get confusing and tiring.

"there may be applications in which an unsigned network is preferable" in which situations will they be preferable.