[*Commutative* diagrams](https://en.wikipedia.org/wiki/Commutative_diagram) usually express path equivalences in a category and thus involve pairs of paths in a category with the same source and target.


[*General* diagrams](https://en.wikipedia.org/wiki/Diagram_%28category_theory%29) - in categories resp. category theory - do not necessarily involve pairs of paths with the same source and target.



> 
> But is there a **name for pairs of paths with the same source and target
> in [quivers](https://en.wikipedia.org/wiki/Quiver_%28mathematics%29)**?  
> Pairs which only eventually are to be called
> "commutative" (expressing equivalence)?  
> ("Diagram" would be a badly chosen name.)
> 
> 
> 


The only commutative closed shapes that are explicitely named are "commutative triangles" and "commutative squares". So I thought about "commutative polygons" but a Google search for ["commutative polygons"](https://www.google.com/search?q=%22commutative%20polygons%22) gave only 10 hits.


Furthermore the question is actually only about a very restricted kind of polygons, maybe "bi-directed" polygons?


If there is no established name, I would appreciate any suggestion.



Pairs of paths with the same source and target
Pairs of paths with the same source and target but with no other nodes in common are called *parallel paths*, at least on the computer science side of things in graph theory -- you can google the term to get some relevant CS papers, but I couldn't find a wikipedia article on parallel paths.


If your paths are allowed to share nodes other than the source and target, I would suggest something like "piecewise parallel paths". With this terminology you can simultaneously get the idea across and score cheap points for alliteration.


As requested in the comments, here is a reference


Jwo et. al., *Characterization of node disjoint (parallel) path in star graphs* (1991) see [here](https://ieeexplore.ieee.org/document/153811).


