The blogger claims no originality of his idea here.
We are given the following diagram:
We would like to classify the nodes by the electric potential there. We label the nodes with 
, 
, 
, etc. where the potential at is larger than that at , the potential at is larger than that at , etc. Therefore we have the following diagram:
Aligning , , and from left to right would give the main current direction. And we put each resistor back in between two consecutive nodes, (e.g., and , and , etc.) according to the two labels nearest to its two ends:
And then the simplification is done.