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The fact that you can represent a graph (the mathematical abstract object) as a diagram is sort of by-the-by here. The most important thing is that graph algor
by owlbite 3y ago
The fact that you can represent a graph (the mathematical abstract object) as a diagram is sort of by-the-by here.
The most important thing is that graph algorithms and concepts have a strong relation to numerical aspects of the linear algebra and can be used to accelerate computation.
(You could of course argue that the act that graphs can be represented as a diagram helps humans come up with such algorithms, but that's basically equivalent to saying that you can represent a matrix as a block of numbers and that helps humans look at it).
- zmgsabst 3y agoI was pointing out the other direction: Diagrams are how you encode categorical models of semantics, which naturally can be represented as graphs. Those graphs can in turn be encoded as matrices. So you have a way to encode semantic foundations as matrices — which you can then use graph algorithms to analyze. Being able to move your semantic models (eg, diagrams) into a computational framework (eg, linear algebra) is neat.