In this video, I introduce the field of graph theory. We first answer the important question of why someone should even care about studying graph theory through an application perspective. Afterwards, we introduce definitions and essential terminology in graph theory, followed by a discussion of the types of graphs you may encounter. We then define several ways to represent graphs as a data structure and finish off the video with a discussion of what types of interesting problems you can ask about graphs to help motivate the ideas in future videos. Typo correction: at 5:12 the vertex set V should be {0, 1, 2, 3, 4} instead of {0, 1, 2, 3, 4, 5} (there is no vertex 5). Big thanks to Dániel László Bertalan for making the closed captions for this video! The sudoku example was inspired by this incredible reddit visualization: https://www.reddit.com/r/dataisbeautiful/comments/6ty4vf/visualizing_the_sudoku_connectivity_graph_more_in/ Support: https://www.patreon.com/reducible This video wouldn't be possible without the open source manim library created by 3blue1brown: https://github.com/3b1b/manim Here is link to the repository that contains the code used to generate the animations in this video: https://github.com/nipunramk/Reducible Music: October by Kai Engel https://freemusicarchive.org/music/Ka... November by Kai Engel https://freemusicarchive.org/music/Ka... Cobweb Morning by Kai Engel https://freemusicarchive.org/music/Ka...