Chapter 1 | The Beauty of Graph Theory

0:00 Intro 0:28 Definition of a Graph 1:47 Neighborhood | Degree | Adjacent Nodes 3:16 Sum of all Degrees | Handshaking Lemma 6:29 Graph Traversal | Spanning Trees | Shortest Paths 11:49 The Origin of Graph Theory 14:10 A Walk through Königsberg 15:34 Path | Cycle | Trail | Circuit | Euler Trail | Euler Circuit 18:47 Euler's Theorems 19:42 Kinds of Graphs 20:05 The 4 Main-Types of Graphs 20:38 Complete Graph 22:10 Euler Graph 22:21 Hamilton Graph 22:41 Bipartite Graph | k-partite Graph 23:42 Disconnected Graph 23:46 Forest | Tree 24:01 Binary Tree | Definitions for Trees 24:47 Ternary Tree 24:59 Applications of Binary Trees (Fibonacci/Quick Sort) 26:15 Complete Binary Tree 26:50 Full Binary Tree 27:02 Degenerated Binary Tree 27:14 Perfect Binary Tree 27:24 Balanced Binary Tree 27:40 Array | Stack | Queue 29:12 Doubly Linked List | Time Complexity 32:07 Binary Search Tree 36:34 Red-Black Tree 38:12 AVL Tree 39:05 Heap 39:45 Heap Sort 41:35 Naive Representation of Graphs 42:27 Adjacency Matrix | Undirected Unweighted Graph 43:27 Adjacency List | Undirected Unweighted Graph 44:17 Representation of a Directed Unweighted Graph 44:38 Representation of Weighted Graphs Blender Models: ▶ Wooden Table: https://sketchfab.com/3d-models/woode... SVG/PNG graphic files: ▶ Some PNG figures have been created with ProCreate ▶ Power Pole: https://lovepik.com/image-450075031/e... ▶ SVG Man Icon: https://www.onlinewebfonts.com/icon/5... Music: ▶ Vincent Rubinetti Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/a... Stream the music on Spotify: https://open.spotify.com/playlist/3zN... ▶ Lullaby - Cooper Cannell ▶    • Free Piano Intro Music - 20 seconds (no co...   Sound effects: https://mixkit.co/free-sound-effects/ Animations have been created with Manim, Blender and Adobe Premiere Pro. Manim: https://docs.manim.community/en/stable/ #graphtheory #graphs #mathematics