# Transform $z$-score to absolute value for visualization

I'm playing with within-module z-score (page 68) which is defined as $$z_i = \frac{k_i - \overline{k}}{SD(k)}$$ where $k_i$ is degree of node $i$ within network module (community). I would like to visualize my network, where diameter of the node will correspond to calculated $z$-score. However, i have no idea how to present negative values on the figure. The first idea that crosses my mind is to compute percentile rank and use it as node's attribute.

Any other ideas?

## 1 Answer

You could try:
$size = e^{z_i}$
Or related:
$size = z_i \;\;\;\;\;\;\;for\; z_i\geq 0$
$size = \frac{1}{-z_i} \;\;\;\;for \;z_i<0$

Edit: reconsidering, my this second method is very bad (it gives very large values for inputs that are just below 0), please ignore it.

• Thanks. Do you have any paper or other reference which I could cite? – Andrej Oct 28 '16 at 9:42
• Unfortunately I don't. I just came up with it off the top of my head. If you really want to credit the idea, you could cite this page suppose. If you want justification, I can't really help you anymore than say that it is a simple smooth function from the reals to the positive reals which is strictly increasing. – dimpol Oct 28 '16 at 10:01