I am looking for a (preferably free) software that can draw braid-related graphs, such as enter image description here and enter image description here

(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 enter image description here)

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 enter image description here?

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    $\begingroup$ What about TikZ? I know its not a drawing software, but its free and once you have learned it you can "draw" everything! $\endgroup$ – aGer Feb 5 '15 at 15:47
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    $\begingroup$ You would have a much higher chance of someone responding with great help on the TeX stack exchange (I've asked TikZ/PGF questions there myself and have always gotten back answer(s)). $\endgroup$ – Daniel W. Farlow Feb 5 '15 at 16:20
  • $\begingroup$ You could use a program like Adobe Illustrator, although it's not free. I've done that with many of my papers. (I've been using TikZ more in recent years since it is a native TeX thing.) $\endgroup$ – Cheerful Parsnip Feb 5 '15 at 20:58
  • $\begingroup$ Maybe you can ask in the Geogebra Forum whether Geogebra may help here. Look for example at this applet of drawing knots. $\endgroup$ – Alexander Konovalov Feb 28 '15 at 19:56

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 :)

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