i have read this tutorial : https://threads-iiith.quora.com/Centroid-Decomposition-of-a-Tree

I didn’t understand the part : "Hence, we decompose the given tree into O(NlogN) different paths (from each centroid to all the vertices in the corresponding part) such that any path is a concatenation of two different paths from this set. (This is the most important/new/extra part in this DS that should be focused on) "

Which NlogN paths? And if possible please explain how we decompose the path from (4 -> 7) in the example tree there!