The map was prepared from a different star catalog than the official map so some star names may be different. The technical documentation states that safe jump routes only exist between stars closer than 3.1 parsecs (10 light years), and the official map is approximately 10.7 parsecs in diameter (35 light years). The official map has unimportant stars removed for clarity, and a few bright stars farther than the limit added for orientation.
I took the HabHyg star dataset, and filtered out all stars farther than 5.5 parsecs from Sol. I tried manually re-naming stars to match the official names (e.g., Gliese 54.1 was re-named YZ Ceti). I then used a utility to create a *.gml file containing each star linked to all other stars within 3.1 parsecs. The *.gml file was loaded into yEd and autoformatted with Organic formatting. There were still parts that were a tangled mess so manual formatting was needed (the original did have some stars removed for clarity). The result was exported as a GIF image.
On the map, yellow boxes are spectral class G, Orange are K, Red are M, Green are F, and white is A. Colony stars have bold outlines. Jump links are labeled with their distances in parsecs.