[Nauty] Canonically labeled output of nauty/Traces actually byte-wise unique?

[Johann Birnick]

Hello,

for my application of nauty/Traces, I'm building a 'database' of some 
data of some graphs in the form of a hashtable. That is, to store data 
attached to some graph, my plan is to canonically label it and then take 
the hash of the canonically labeled graph and then store some data 
(think: graph invariants) of the graph in a hashtable.

For this, it would be important to know if the canonically labeled graph 
which is returned from say Traces is guaranteed to be unique up to 
actual byte representation?

More precisely: Take two isomorphic graphs. For each of them, 1. call 
Traces and get a `sparsegraph` object which is the canonically labeled 
graph, and then 2. compute the hash of this sparsegraph. Will the hashes 
be the same?

(It doesn't seem like it, as in the example programs always `aresame_sg` 
is called, which seems to do some nontrivial things such as skipping 
certain bytes.)

If not, then are there perhaps special cases in which it will be 
guaranteed? For example, say my two graphs really use the same number of 
vertices (i.e. have no dead vertices of degree 0) and same number of 
edges. Will it work in this special case?

Thank you very much in advance!

Johann