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lexprod · NOT not a title

Hey!

So I know little about graph theory aside that they deal with the designs where there are lines and nodes. Recently Big Brother featured a puzzle I helped work on that reminded me of those diagrams. One of the things we had to decide was how to arrange the dots, and wondered if there was some graphically optimal, or even just prettier, way to arrange the circles, while maintaining the correct bonds shown. Also keeping the same size of the circles and bonds, for visibility.

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I'll have a P please...

L'lanmal · Daedalian Member

I notice that you already have all the connections as straight lines, but the first graph theory result of interest to aesthetics that comes to mind is http://en.wikipedia.org/wiki/Fáry's_theorem .

Dual graphs are also good to consider when trying to give a novel presentation of well-known data. http://en.wikipedia.org/wiki/Dual_graph

L'lanmal · Daedalian Member

As for your particular graph, I would imagine an artist would help more than a mathematician, so that's the approach I'd take. If it helps, it is a "bipartite" graph however, meaning you could split it into two halves with no internal edges in either half. I don't think this is what you are looking for.

Personally, I'd approach it by making the loops as convex as possible to form a nice (alternating) border, then have the dead-ends fill the insides of the loops. But this isn't based on any academic theory I know of.

The Potter · Feat of Clay

I would attempt to make the connecting lines approximately the same length. Or a long, medium and short length. Avoiding overly straight segments of connected dots was a good idea.
The bottom right corner is particularly weak-- the placement of the purple dots directly below the green ones created a sawtooth.
The top right is nice-- except the purple dot below Hosted A Competition is too high.
I like the left side much more. Even though it is more crowded.
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Artwork | Fractals | Don't ignore your dreams; don't work too much; say what you think; cultivate friendships; be happy.

Elethiomel · Daedalian Member

Check out http://www.graphviz.org/ for some tools and theory on this.