Why I don’t like graphs for thinking

Discussing this with a colleague some time ago, in the context of architectural diagrams for a system, I said that graphs provide an illusion of understanding. The moment you have to fully explain or implement what the graph describes, trouble starts.

To me, graphs can bring the point home, but only if the point is already made. Graphs should only illustrate things that are more thoroughly expressed in text.

If you have a good counterargument, I would love to hear it!