Lesson Plan
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Elmwood Park High School: Vertex Edge Graphs

For Students 10th - 12th
In this Unit, you will use vertex-edge graphs and Euler Circuits to help find optimum paths. Included are two lessons that help you develop the understanding and skill needed to solve problems about optimum paths and conflicts.
Interactive
National Council of Teachers of Mathematics

Nctm: Illuminations: Graph Creator

For Students 3rd - 8th
Use this vertex-edge tool to create graphs and explore them. Investigate ideas such as planar graphs, complete graphs, minimum-cost spanning trees, and Euler and Hamiltonian paths.
Article
Other

Free Codecamp: How to Think in Graphs

For Students 10th - 12th
In this article, we're going to demonstrate various applications of graph theory. These applications will contain detailed illustrations. As the author states, if you've been looking for a "graph theory and everything about it tutorial...