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:

SVG/PNG graphic files:
▶ Some PNG figures have been created with ProCreate

Music:
▶ Vincent Rubinetti
Download the music on Bandcamp:
▶ Lullaby - Cooper Cannell

Animations have been created with Manim, Blender and Adobe Premiere Pro.

#graphtheory #graphs

[pranavsinha]

For once youtube recommended something so underrated yet so awesome, loved every second of this!

[GAURAVSINGH-yidp]

i don't generally comment but: its a wonderful video i am amazed how you would have created such a complex video, must have used Manim, also it would have taken lot of research. cant believe that i am the first person to comment. thanks for this video it created a spark of interest in me for learning more about the topic as my university is teaching me. anyway thanks for this video and i hope your video and channel grows. ❤ Love from India 🇮🇳🕉.

[kialim]

I like the fact you included the history of graph theory in the video. Not even introductory texts do that.

[Gasahorlogo]

An amazing high-quality video. This was very helpful, thanks.

[firephoenixgamers]

Great video. Would recommend as a refresher for any student taking an advanced algorithms course or even discrete math

[dyllanusher]

Anyone that posts a 45 minute manim animation about math immediately has my subscription. I don't even care what subject it was in! :D

Lovely video btw :)

[singhabhishek]

Excellent one. Can't wait for chapter 2. For undirected unweighted graph, Adjacency Sets instead of Adjacency Lists are also helpful.

[umar]

Please keep producing more content like this? It is such a wonderful supplement to my math studies!

[davidpersson]

This channel only having 920 subs is absolutely criminal

[elrisitas]

Amazing work, the quality of the video is fabulous! Thank you for this masterpiece

[OLApplin]

I don't remember when I first heard about graph, but we studied them in my CS degree and they quickly became one of my favorite topic in math and CS

[crux]

Feels lucky to be an early viewer. Manim animations are so cool 🥹

[wonjontheaxolotl]

this is beautifully animated and you put in so much work doing this AMAziNG JOB

[jayeff]

You broke it down to very understandable bits and supported them with animations showing the points very clearly. Well done!

[EnterichOfs]

This was incredible, waiting for part 2!!

[snk-js]

I am not Computer science student, I am a programmer, but I love to watch every single graph theory tutorial in YT, i have watched many,
after sometime I started to notice how teachers lecture the graph theory and how, in which order they introduce the theme and which illustrations or animations they use.
It's simply fascinating that graph theory pushes teachers forward to animate didactically, I wonder one day to be one of them.

[phobosmoon]

what an amazing video lecture! Ty very much!

[zerojuan]

Very well done introduction to graph theory, the visuals were key to following the concepts and building intuition. Can't wait to see what you have in store for the following chapters!

[UndyingEDM]

I knew from the start I'd want to watch the whole thing, so I set aside some time and I did! I think everyone should appreciate those moments when the animation plays and lets whatever you have just learned to sink in. Excellent presentation. Universities should start taking notes before they become obsolete lol

[bennyloodts]

Clear amd to the point: great work. Respect!