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A relation between two sets $A$ and $B$ is a subset of $A \times B$. If taking a multiset subset of $A \times B$, e.g. allowing $(a,b)$ appears twice in the subset, is there a name for such a generalized concept for relation?

An example will be the edge set of a directed multigraph.

thanks.

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Yes, there is :)

In fact, it's one of your tags!

If we have multiple occurrences of related elements, then we essentially have multiple edges between those elements viewed as vertices. These edges have no labels.

Hence, a mutliset relation is a directed graph with parallel edges allowed.

Hope that helps :)

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