What software is used to draw undirected graphs?

Try Graphviz.

If you use $\LaTeX$, tikz is very nice for making graphs (I use it all the time to make commutative diagrams).

Otherwise one could use pretty much any vector graphics program, for example the free (as in freedom and in beer) inkscape.

There's also dia, though it is more for UML-like diagrams.

Sage can generate graphs. It's like Mathematica/Maple but it's open source and free.