What software tool should I use to draw graphs?

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I am writing a latex document, and I have a technical lemma that I would like to illustrate with an image.

The field is graph theory, and the lemma has several cases, so I want to draw a chart detailing the cases and to draw a picture of a graph for each case. The image has to be jpg or some other format that latex can handle, because I want to embed it in the document.

What would be a good software tool to do such a thing?

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See TikZ examples of graphs, you can also just draw it in LaTeX :)

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I think Wolfram Mathematica is a good software to do some graphs. I think matlab will do that for your purpose too!