I've been exploring the concept of antisymmetry in DiGraphs within SageMath and noticed a discrepancy between the standard mathematical definition of an antisymmetric relation and SageMath's implementation for DiGraphs. I'm looking for some clarification or insight into this observation.

The standard definition of antisymmetry in a relation R states: if aRb and bRa, then a=b. In contrast, Sage seems to interpret antisymmetry for DiGraphs in a way that emphasizes the absence of reciprocal paths, which is more restrictive. To illustrate, I ran a few tests within a SageCell to understand how antisymmetric() behaves with different graph configurations: A graph with a loop and no reciprocal edges, which should be antisymmetric: ``` DiGraph([(1, 2), (3, 1), (1, 1)], loops=True).antisymmetric() # Expected True, Returns True ``` A graph with a direct reciprocal relationship (1,2) and (2,1), clearly violating antisymmetry: ``` DiGraph([(1, 2), (2, 1), (3, 1), (1, 1)], loops=True).antisymmetric() # Expected False, Returns False ``` This third example is interesting because, under the standard mathematical definition, antisymmetry focuses on direct reciprocal relations between pairs of elements, not the existence of a path between vertices. Therefore, a cycle does not inherently violate antisymmetry unless there are direct reciprocal edges between any two vertices in the graph. ``` DiGraph([(1, 2), (2, 3), (3, 4), (4, 1)]).antisymmetric() # Expected True, Returns False ``` Is SageMath's antisymmetric() method intentionally designed to consider the broader structure of the graph by evaluating paths rather than just direct edges to determine antisymmetry? It would be great to get some clarification on this and understand the rationale behind SageMath's implementation choice. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/88c4e8f1-f04d-4010-91b4-39fdd8a403f8n%40googlegroups.com.