We need to draw many graphs in scientific papers. These graphs are the very important parts of a paper that makes it understandable. I want to know what is the best way of drawing nice, complete and understandable graphs?
I don't know if it's the best since I haven't tried everything available. But, I have had a lot of success using Matlab to generate figures, saving them as eps files, and including the eps files within a Latex document using WinEdt. I think most journals prefer (or at least accept) Latex documents, so using Latex is a good idea in general.
If you are creating graphs from scratch (i.e. aren't trying to convert an existing electronic representation such as a. jpg file) then Matlab is a good choice, but there are no doubt many other choices that are just as good. If you already have an existing electronic representation of a graph, you can use Adobe Acrobat (standard version) to convert it to an eps file.
Latex can be purchased, but I've been using a free version for years called Miktex which I like very much. I personally don't see the need to purchase Latex since Miktex works so well.
Although you can use any text editor you like for editing Latex documents, I think it will be worth your while to get WinEdt, which is specially designed for this. Again, I'm sure there are others Latex editors that are as good, but WinEdt is a great choice in my opinion.
There is also the issue of creating quality PDF files. Although there are several ways to create PDF files (e.g. Sumatra is free and works great as a previewer with WinEdt), I have found that using WinEdt to create a postscript file (.ps file) and then applying Adobe Acrobat (standard edition) will create a high quality PDF file. As mentioned above, Adobe Acrobat can also convert existing graphs stored in a variety of formats to eps files.
In summary, I use Matlab, Mixtex, WinEdt, Sumatra (for previewing), and Adobe Acrobat. If you're not familiar with some or all of these, it may take you a while to learn how they all work together, but I feel that it's well worth the time spent.
You may want to clarify this: Are we talking charts (e.g., column chart, scatter plots), or graphs (e.g., K_4)? This may significantly change how one answers this question.