On Mon, Mar 11, 2024 at 9:24 PM Samuel Lubliner <samlubli...@gmail.com> wrote:

> 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 > ``` > > you can check the docs, and see that Sage, essentially, calls directed acyclic graphs antisymmetric. I.e. if there is a path from x to y then there is no path from y to x (assuming x!=y) A graph represents an antisymmetric relation if the existence of a path from a vertex `x` to a vertex `y` implies that there is not a path from `y` to `x` unless `x = y`. that's a more interesting, mathematically, definition, than mere absense of loops of length 2. > 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 > <https://groups.google.com/d/msgid/sage-support/88c4e8f1-f04d-4010-91b4-39fdd8a403f8n%40googlegroups.com?utm_medium=email&utm_source=footer> > . > -- 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/CAAWYfq3o9S5Kj6OzA1xW0f0n4KObmfWgACsTk9nkR-D1zOx%2BNw%40mail.gmail.com.