This graph gives a quick way to visualise all HSK words. Words are coloured by HSK level. More common words are closer to the centre of the graph. You can download a high resolution version from this page.
I have uploaded a few HSK word and character graphs. See the Graphs Download page for high resolution poster-sized images  and graph files that you can use.

Most of these images are quite pretty, and some might even be useful to help learners to visualise which words share characters, etc. I am currently using the HSK 1-2 and 1-3 word charts to study for HSK levels 2 and 3.

These graphs were generated by a script that I wrote in Python. HSK word lists came from Word frequencies, which were calculated from subtitles, are from SUBTLEX-CH. Character frequencies and composition are from distributed node weight (DNW) data. The graphs were drawn using Gephi and Graphviz. Some pinyin data came from the free Chinese dictionary CC-CEDICT.