It's a bit of a mess, but its also pretty cool, no? The full version is here, with which you can zoom and pan around. As usual these dense graphs are a bit too noisy to be useful, but it gives you the sense of what this connection data does for you.

There are so many different ways to prioritize which words to include, which words to link. This graph is made from the official HSK Level 1 words, then simply linked to their immediate children. I also included the frequency rank of each word in parenthesis. I put together some other possible graphs like this, not totally sure where to go from here.

Previews of ther possible graphs