Video 2

This video explains walks, trails, paths, circuits, and cycles in graph theory.
In graph theory, a walk is defined as a sequence of alternating vertices and edges, like Vertex 1, Edge 1, Vertex 2, Edge 2, etc. Walks are how we traverse a network. In a walk, you are allowed to repeat edges and vertices as many times as you'd like. A trail, on the other hand, is a walk in which you do not repeat edges. And a path is a walk in which you do not repeat edges and you do not repeat vertices (note that the set of paths in a graph is a subset of trails in that graph).