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The DOT markup language uses -> and -- to indicate directed and undirected edges between nodes. Do you know of any other programming or markup languages with graph operators, and are there any standards, conventions or even just trends for defining nodes and edges?

A: 

The Ordered Graph Data Language uses whitespace for defining edges. It only supports directed graphs, if you want an undirected graph you will ever have to implement direction-agnosticism in your app or write down every edge twice.

yUML is not a general-purpose graph description language, it only supports UML Activity Diagrams, UML Use Case Diagrams and UML Class Diagrams. Similar to DOT, it uses an iconographic ASCII art representation of the edges. For example, the graphical representation of an aggregation association is a hollow diamond at the end of the edge. yUML represents this using <>. So, an aggregation association between A and B would be written as [A]<>-[B] and rendered as [A]<>-[B]

And then there's GraphML.

Jörg W Mittag