algorithm - Understanding Nauty algorithm

Question

I am trying to understand the Nauty algorithm. Following this article: http://www.math.unl.edu/~aradcliffe1/Papers/Canonical.pdf
In this algorithm the vertices are distinguished based on their degree and the relative degree of a group corresponding to other groups(group action). In this way we get the groups as:

1379|2468|5
After this step, splitting is done as mentioned in this paper - page 7. One image from this article is:

I am unable to understand how the splitting is done from 1379|2468|5 to 1|9|37|68|24|5 Why 1 and 9 went to different groups and 37 went to another group.

Answer 1

Briefly, you are individualizing vertices and then 'shattering' the cells of the resulting partition until the partition becomes equitable.

As it says in section 5:

Having reached an equitable partition, we need to introduce artificial distinctions between vertices

This is described in definition 9. So we have chosen {1} from the cell {1379} and then refined the resulting partition until it is equitable (see definition 6 and the example below it).

Thus cell 1 - {1} - shatters cell 3 - {2468} - into two cells {68|24} due to 1 having 0 neighbours in {68} and one in {24}. Similarly, {379} is split by {24} into {9|37}.