On Friday 15 March 2024 at 15:08:34 UTC-7 Hellen Colman wrote:

Let me just clarify the main point of his question just in case we can 
still obtain a helpful answer. Essentially the question is: Why is Sage 
calling "antisymmetric" to a property that is not the standard 
antisymmetric property?


I agree that a relation gives rise to a graph, but I wouldn't presume that 
the standard notion of "antisymmetric" for relations would agree with that 
on graphs (or even that there would be a property of graphs that is called 
"antisymmetric).  So if there is something transferable to be learned for 
for students here it is perhaps that terminology is not perfectly aligned 
between different areas in mathematics. Given that the word "antisymmetric" 
is now taken to mean something specific for graphs (I assume whoever did 
that consulted some graph-theory books), it will have considerable inertia 
because changing it to something else would break backward compatibility.

If you feel strongly that a change in terminology would be beneficial, you 
could collect some references corroborating your proposed meaning. If 
someone else feels strongly enough about preserving the present meaning, 
they would likely counter with their own set of references. At that point 
hopefully a consensus would grow, with a (slight) preference for the status 
quo. If both notions have support, we'd likely look into a way of 
supporting both; probably by dangling the appropriate adjectives in front 
of "antisymmetric", like "edge_antisymmetric" and "path_antisymmetric" or 
something like that.

For your research, you might be interested in an 
is_homotopically_equivalent method.

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