Good summary list. For most developers, there is a nice abstraction barrier for graph theory because tools like neo4j, efficient RDF stores, search libraries, etc. make it fairly easy to build apps without getting one's hands dirty in the details. (But knowing the details makes it more likely to get creative and novel apps.)

Off topic, but: since so many things are well described as graphs, the GraphViz tool is great for communication: few lines of code to write your data to a 'dot' file, and a few seconds later you have a visual representation of your data.