Does all of percolation theory ignore “node width” or is it sometimes assigned a number – say a probability?

Ok so it’s May 18.
In a comment on May 15
https://www.facebook.com/kenneth.udut/posts/10100275531374938
 
I wrote:
“c) edges (as in edges and nodes) don’t _seem_ to have an inherent inbetweenness in the width direction but only in the length. HOWEVER.. it may have been abstracted too far? will have to return to this.”
 
Now to today:
Percolation Theory examines edges and nodes.
It comes from the study of liquids percolating through dirt, or panning gold and such.
 
I’ve studied it before but not thoroughly and not with this question:
Does all of percolation theory ignore “node width” or is it sometimes assigned a number – say a probability?
 
https://www.scientificamerican.com/article/the-mathematics-of-how-connections-become-global/

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