Does NEAT require only connection genes to be marked with a global innovation number? Does NEAT require only connection genes to be marked with a global innovation number? 

From the NEAT paper


  Whenever a new gene appears (through structural mutation), a global innovation number is incremented and assigned to that gene.


It seems that any gene (both node genes and connection genes) requires an innovation number. However, I was wondering what was the node gene innovation number for. Is it to provide the same node ID across all elements of the population? Isn't the connection gene innovation number sufficient?  

Besides, the NEAT paper includes the following image which doesn't show any innovation number on node genes.
It is actually the other way around: connection IDs is what is debated!

Nodes always have innovation IDs (in the image, it is just their identifying number).

Node IDs are sufficient to identify connections. If a connection links nodes 3 and 6, then it is the same as another connection linking nodes 3 and 6: no need for an extra ID. So why the extra innovation IDs then?

On the one hand, this is an implementation choice: maybe these extra IDs would allow you to create a more complex but faster code?

On the other hand, there is a debate around whether a connection between two nodes means the same thing at different times in evolution. If you have no innovation IDs, then you cannot tell apart an old connection from 3 and 6 and another that was independently created later in a different genome (imagine the old connection was removed first). Is this relevant? As said, it is an open debate. Surely, it is not crucial at a basic level!

This question (and my answers) is related to this other question on Stack Overflow.