I would like to model a graph where each vertex connects to a different type. Below is an example of the kind of thing I'm after. In effect, the red nodes are acting as kind of "super edges" that connect multiple vertexes together.
If additional context is required, this is modelling various parts of various production chains. The blue vertexes represent some ingredient or product and the red vertexes represent various processes that can transform some amount of inputs into some amount of outputs. The edge weights describe the ratios of these processes.
The term you are looking for [if there are two types of vertices as you defined] is bipartite graph: every edge is between a red vertex and a blue vertex.