I was pointing out the other direction: Diagrams are how you encode categorical models of semantics, which naturally can be represented as graphs. Those graphs

I 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.