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Graph theory question

Hello all,

I am working on a problem that appears to be most easily solvable using graphic theory. My problem is that I have never even dabbled into this thicket and would like to have a cookbook that, through some examples, would show me how to start a learning process, which should be as brief as possible. I saw that there exist Matlab packages (have downloaded one but stuck it in a vase to be admired from afar) but I would need a hand to lead me through the early stages.

With great appreciation for any advice,