This is what the diagram represents with the building blocks substituted in. Although there’s a technical term for this, called a colimit, we informally call this gluing building blocks along shared boundaries (which are, in this case, those isolated vertices).
Structural mathematics allows us to have a good understanding of what this gluing process is even without knowing what is inside the bubbles and the junctions. We didn’t have to know much about the internal structure of a triangle or how it was constructed to do this - we simply stated how these existing things were related to each other, something external to the graph building blocks. We just declared what we wanted as a piece of data, rather than writing another piece of hacky code that will become someone else’s problem to debug down the line.