The central star should be coloured:
Indigo (dark blue)
The reason is, that if you draw a hexagonal grid across everything like this (excuse the sloppy photoshop work):

Then, for any given dot, you simply:
count up the number of dots on any of the intersecting lines, which will always give the same sum, based on the colour of the dot you chose:
Red - 0
Orange - 1
Yellow - 2
Green - 3
Blue - 4
Indigo - 5
Violet - 6