Chapter 1 | The Beauty of Graph Theory

0:00 Intro 0:36 Definition of a Graph 1:55 Neighborhood | Degree | Adjacent Nodes 3:24 Sum of all Degrees | Handshaking Lemma 6:37 Graph Traversal | Spanning Trees | Shortest Paths 11:57 The Origin of Graph Theory 14:18 A Walk through Königsberg 15:42 Path | Cycle | Trail | Circuit | Euler Trail | Euler Circuit 18:55 Euler&Theorems 19:50 Kinds of Graphs 20:13 The 4 Main-Types of Graphs 20:46 Complete Graph 22:18 Euler Graph 22:29 Hamilton Graph 22:49 Bipartite Graph | k-partite Graph 23:50 Disconnected Graph 23:54 Forest | Tree 24:09 Binary Tree | Definitions for Trees 24:55 Ternary Tree 25:07 Applications of Binary Trees (Fibonacci/Quick Sort) 26:23 Complete Binary Tree 26:58 Full Binary Tree 27:10 Degenerated Binary Tree 27:22 Perfect Binary Tree 27:32 Balanced Binary Tree 27:48 Array | Stack | Queue 29:20 Doubly Linked List | Time Complexity 32:15 Binary Search Tree 36:42 Red-Black Tree 38:20 AVL Tree 39:13 Heap 39:53 Heap Sort 41:43 Naive Representation of Graphs 42:35 Adjacency Matrix | Undirected Unweighted Graph 43:35 Adjacency List | Undirected Unweighted Graph 44:25 Representation of a Directed Unweighted Graph 44:46 Representation of Weighted Graphs Blender Models: SVG/PNG graphic files: ▶ Some PNG figures have been created with ProCreate Music: ▶ Vincent Rubinetti Download the music on Bandcamp: ▶ [11:57 - 14:06] Lullaby - Cooper Cannell Animations have been created with Manim, Blender and Adobe Premiere Pro. #graphs