Bryan, Have a look at videos from Darren Crowdy from a couple of years ago . Start at video #1 and go from there. I assume you are already reading Wai-Kai Chen's "Graph Theory and Its Engineering Applications", Gilbert Strang's many books on the topic, and books by Chartrand, Zhang, and Lesniak, Gross, Yellen, and Anderson, etc. You should write about where you are at. I've written maybe a dozen answers here. This is one such.
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