When I create graphs, I want to create nodes and connect them first, without caring too much about design yet. When I am done, I like to move things around to make the graph more visually appealing. yEd caters precisely to my needs by separating the mathematical graph (nodes, edges) from the graphical representation attached to these entities.
In particular, yEd does _not_ allow for edges to exist without connections to nodes. In other editors (draw,io, Visio, ...), an edge might look like it was connected to a node visually, but it is actually free-floating. This quirk rules out any subsequent automated analysis.
Finally, yEd does a tremendous job at laying out graphs with a plethora of tweakable algorithms.
All in all, I am about thrice as productive with yEd than with all other graph editors I know.
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