What is Graph Theory? This video introduces you to graph theory. It will give you an overview of what it is. Graph theory is a branch of mathematics within discrete math that is not only super fun to study for its own sake, but also incredibly useful in disciplines such as network analysis and network science, medicine, computer science, and engineering. Graphs can be used to represent networks of people, computers, and abstract relationships. Graph theory is about pairwise relationships (edges) between objects (vertices). Our graph theory introduction will teach you about the diameter, distance, and degree of graphs and some different types of graphs. At the end of the video, I will present a challenge that I found fascinating involving the graph theory concepts from earlier in the video. I invite you to post your favorite graph in the comments and to discuss graph theory with each other. Let me know if you have any questions or suggestions, and have an awesome day! Reddit: https://www.reddit.com/r/Vitalsine/ Discord: https://discord.gg/dvpXxBy Some links for additional discovery: Centrality and Graph Theory (one of the most important uses of graph theory!): https://www.youtube.com/watch?v=HFP4Br7uvYo https://en.wikipedia.org/wiki/Graph_theory#:~:text=In%20mathematics%2C%20graph%20theory%20is,also%20called%20links%20or%20lines). http://discrete.openmathbooks.org/dmoi2/ch_graphtheory.html http://www.openproblemgarden.org/category/graph_theory http://dimacs.rutgers.edu/~hochberg/undopen/graphtheory/graphtheory.html ... https://www.youtube.com/watch?v=N_tJo3XwY-M

What is Centrality? This video will introduce you to centrality and give you an overview of what it is and where it used in the real world. Betweenness centrality, closeness centrality, and degree centrality are covered in this video. This video is all about measuring the importance of nodes in a graph using centrality indices. This is also the second video in the discrete mathematics series and the first video about graph theory on the channel. Why does centrality matter? Because networks are everywhere, and centrality gives us crucial information about networks. Ever wonder how websites are ranked? Centrality is highly relevant to many sciences and is an interesting mathematical concept in and of itself. I encourage you to talk about centrality in the comments and to devise algorithms to determine centrality as well as debate the drawback (or benefit) that different centrality measures can identify different nodes as being "most important." Thank you so much for watching. Have fun thinking about math! If you enjoyed the video, please consider watching my other videos in the graph theory series: https://www.youtube.com/playlist?list=PLZ2xtht8y2-Jx8hxFvnFQfEej1PzqFbVX Reddit: https://www.reddit.com/r/Vitalsine/ Discord: https://discord.gg/dvpXxBy ... https://www.youtube.com/watch?v=HFP4Br7uvYo

This video covers strong hypergraph colorings. We will go over several examples, as well as draw several connections to graph theory, including to graph squares and distance-2 colorings. We also discuss applications to communication networks. Communication Network Application Resources: https://www.ru.is/faculty/mmh/papers/strongcol.pdf https://link.springer.com/chapter/10.1007/978-3-540-75520-3_46 https://link.springer.com/book/10.1007/978-3-319-60469-5 Recommended Books: ******************************** Hypergraph Theory ******************************** "Hypergraph Theory: An Introduction": https://amzn.to/43bC8h1 "Introduction to Graph and Hypergraph Theory": https://amzn.to/3Ij9Poz ******************************** Graph Theory ******************************** "Introduction to Graph Theory (Trudeau)": https://amzn.to/43e2gHR "Graph Theory (Diestel)": https://amzn.to/3OuLxfw "The Fascinating World of Graph Theory": https://amzn.to/3pSUFQB ******************************** Misc. Undergraduate Mathematics ******************************** Discrete Mathematics with Applications (Epp): https://amzn.to/3MBXzkL A Book of Abstract Algebra (Pinter): https://amzn.to/3On2jgp Language, Proof and Logic: https://amzn.to/3Oi68n6 Linear Algebra and Its Applications: https://amzn.to/3MhvM91 All the Math You Missed: https://amzn.to/42FqOK5 These are my Amazon Affiliate links. As an Amazon Associate I may earn commisions for purchases made through the links above. 0:00 Definition 1:05 Strong Chromatic Number 2:30 Distance-2 Colorings and Graph Squares 5:55 Applications #hypergraph #hypergraphs #vitalsine ... https://www.youtube.com/watch?v=2uz9CNHM1dQ

This video introduces clique complexes, a type of abstract simplicial complex. We will cover several examples and special cases of clique complexes. We'll go over the relationship between clique complexes and conformal hypergraphs, as well as certain requirements that clique complexes must satisfy. This video will also introduce independence complexes. Both independence complexes and clique complexes are abstract simplicial complexes that are built from a simple graph. ... https://www.youtube.com/watch?v=Aoh4haV7Ekc