Hey! Sorry to bother you again, but I'm still having problems understanding how NestGraph[] builds the tree.

I understand the function and how it generates the lists, I just don't get how NestGraph[] traverses the lists?! Please find attached a note I created to understand the flow.

My questions (please see attached image):

1. How does NetGraph[] figure out to go from {1,3} to {2,6}?
2. Are the list entries I tagged with a question mark not evaluated at all?

I think I'm having problems seeing something obvious and in the end it's probably easy, but I really like to understand.

Thank you very much!

The argument to the pure function is {2, 3}, which is assigned to #

2 {2, 3}
(* {4, 6} *)

2 {2, 3} + 1
(* {5, 7} *)

Compare the output of the following for different values of n

NestList[{2 #, 2 # + 1} &, 0, n]

NestGraph[{2 #, 2 # + 1} &, 0, n, VertexLabels -> All]

and you should be able to see how the graph "grows".