Guide to Walks, Trails, Paths, Circuits, and Cycles! [Graph Theory Tutorial]

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). I think it's important to know that some authors do define these terms slightly differently; some refer to what we just called a 'trail' as a 'path' as well, while referring to what we called a 'path' as a 'simple path' instead. Here are some links for more information: https://www.geeksforgeeks.org/mathematics-walks-trails-paths-cycles-and-circuits-in-graph/ http://mathonline.wikidot.com/walks-trails-paths-cycles-and-circuits https://mathworld.wolfram.com/Walk.html Recommended Books: ******************************** Hypergraph Theory ******************************** "Hypergraph Theory: An Introduction": https://amzn.to/48WKqfy ******************************** Graph Theory ******************************** "Introduction to Graph Theory (Trudeau)": https://amzn.to/48ZWhtj "Graph Theory (Diestel)": https://amzn.to/4aYCSdW ******************************** Misc. Undergraduate Mathematics ******************************** Discrete Mathematics with Applications (Epp): https://amzn.to/4aWC1dM A Book of Abstract Algebra (Pinter): https://amzn.to/3S2QmfV Language, Proof and Logic: https://amzn.to/47EIZkE Linear Algebra and Its Applications: https://amzn.to/48QsoMt All the Math You Missed: https://amzn.to/3u5dORP These are my Amazon Affiliate links. As an Amazon Associate I may earn commissions for purchases made through the links above. 0:00 - Graph Walks 0:53 - Graph walks as lists 1:35 - Trails 2:50 - Circuits 3:30 - Paths 4:50 - Closed paths = Cycle 5:30 - Summary 6:44 - Real-world Example 7:35 - Traveling Salesman Problem