Let's imagine your cluster as a tree with the following levels:
- Abstract global root (Top or root)
- Data centers (1st level)
- Racks (2nd level)
- Nodes (3rd level or leaves)
If we draw this tree there should be something like this:
Let's count distance between any circle and its parent as 1.
Then the distance between any two circles is the sum of their distance to their closest common ancestor or 0 for the same node.
So it's always 6 for any two nodes in different data centers (like between /d1/r1/n1 and /d2/r4/n10).
"The distance between two nodes is the sum of their distances to their closest common ancestor" (Hadoop: The Definitive Guide 4th ed, page 70)
distance (/d1/r1/n1, /d2/r3/n10) = 6
The common ancestor between two nodes is /
so the distance from n1 to / is 3
and the distance from n10 to / is 3
the total is 6
Hope this helps you :)