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.

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