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I disagree about the graph theory as well. Unless you are doing things with learning on networks you won't need it.

I think a solid background in linear algebra, multivariate calculus, and convex optimization will take you really far.

A lot of data is best represented graphically, and while you can shoehorn this sort of data into a vector space by projecting using a graph distance metric, the results are likely to be inferior.

I agree a lot of data can be represented graphically, but if you look at the literature it mostly is getting shoehorned into vector spaces. This doesn't mean people shouldn't learn about Graph Laplacians and friends, but I don't think it's an entry requirement.

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