I am looking for a (preferably free) software that can draw braid-related graphs, such as 
and 
(Quoted from A Study of Braids By Kunio Murasugi, B. Kurpita)
I have seen this question, but the answers given seem not very helpful for my case; for example, I found it not so easy to draw a cube or a braid in Geogebra. Also, I can draw braids with the braid package as is explained here,
(for example, something like 
)
but I don't know how to modify the graphs so that it looks like the pictures above. Also, how about braids with $n$ strands for a general $n$, such as 
?
I used Inkscape a lot for my thesis, which has a path effect for drawing knots. It is - at least in the version I have - extremely buggy, but if you never ever change the path while the knot effect is turned on, it works :)