GraphThing is a tool that allows you to create, manipulate and study graphs. These "graphs" are mathematical objects (look at this introduction to Graph Theory) that describe relationships between sets; they are not 2D plots, charts, or anything similar to that.
If the image on the right means nothing to you, you're probably at the wrong place.
That means that not only does it cost you nothing, but you also have the freedom to redistribute it or modify it however you please, so long as you also give these freedoms to others.
As an example, the CityBuilder project has taken a particular version of GraphThing, and modified it for their own needs. They have released the source code to their forked version under the GNU GPL.
Here are some key features of "GraphThing":
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