Graph Theory – Best Software for Drawing Undirected Graphs

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I need to make a nicer-looking version of this image:

Undirected graph with crappy loop

Is there some program that generates these graphs? Or are they done by hand in something like Visio?

(I'm on Mac OS X, and I have access to Windows if needed)

Best Answer

Try Graphviz.

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[Math] Find All NonIsomorphic Undirected Graphs with Four Vertices

There aren’t all that many, and yes, you can go through the possibilities from $0$ edges through $\binom42=6$, the maximum possible. I’ll get you started.

$0$ edges: $1$ graph:

       *   *   *   *

$1$ edge: $1$ graph:

       *---*   *   *

$2$ edges: $2$ graphs, because the edges can be disjoint or share a vertex:

       *---*   *---*                     *---*---*   *

$3$ edges: The edges can’t all be disjoint: that would require $6$ vertices. Thus, we must have

       *---*---*

as part of any such graph. There are $3$ possibilities:

       *---*---*---*                  *---*---*                *---*   *  
                                          |                     \ /  
                                          *                      *

Can you see why no two of these are isomorphic, and why they are the only possibilities?

I’ll leave the rest to you for now. There are very few non-isomorphic possibilities for $6$ edges and for $5$ edges, so perhaps you should start with those cases. The only case that should take a bit of work is the case of $4$ edges.

Best Answer

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