How I built the SoME3 voting system with graph theory

I will explain to you how to create a voting system for a massive competition using graph theory. This is how I developed the algorithm for the Summer of Maths Exposition competition. I will explain all the principles starting from scratch. We will cover the following concepts: what is a graph, the diameter of a graph, the adjacency matrix of a graph, the concept of an expander graph, the expansion rate of a graph, and its impact on the graph's diameter. 00:00 Introduction 00:54 Naive approach and three criteria 05:13 Mathematical approach 07:18 Three examples of the expansion rate concept 10:00 How to construct a good expander graph? 12:19 Conclusion and final example Thanks to James Schloss and Grant Sanderson for all the organization. Links: Video excerpts SoME 2:    • What makes a great math explanation? | SoM...   Fouloscopie:    • 4 expériences sociales pour comprendre les...   Articles Social Choice: https://en.wikipedia.org/wiki/Social_... The Anatomy of the Facebook Social Graph: https://arxiv.org/abs/1111.4503 Analyzing Twitter User Network: https://towardsdatascience.com/analyz... Expander graph: https://en.wikipedia.org/wiki/Expande... Alon-Boppana bound: https://en.wikipedia.org/wiki/Alon%E2... Joel Friedman's proofs of Alon's conjecture: https://arxiv.org/abs/cs/0405020 Websites Six Degrees of Music Separation: https://www.whosampled.com/six-degrees/ SoME 3: https://some.3b1b.co/ Source code of the platform https://github.com/fcrozatier/champagne #some3