Introduction to Hypergraphs [Graph Theory]

This video introduces hypergraphs with plenty of examples. We will cover terminology and basic properties of hypergraphs. Hypergraphs are a generalization of graphs, where edges are allowed to link more than 2 or fewer than 2 vertices at a time. There exist notions of degree, regularity, subgraphs, and adjacency in hypergraph theory just like in graph theory, and the concept of incidence is especially significant in the theory of hypergraphs. The concept of dual hypergraphs, which we cover at the end of the video, is also very significant in the study of hypergraphs, and will be revisited in future videos.

Thanks for watching! If you'd like to learn more about hypergraphs, I highly recommend these resources:

BOOK: https://link.springer.com/book/10.1007/978-3-319-00080-0

BOOK: "Introduction to Graph and Hypergraph Theory" by Vitaly I. Voloshin

Interesting paper: https://epjdatascience.springeropen.com/articles/10.1140/epjds/s13688-020-00231-0

Great discussion on Math Overflow: https://mathoverflow.net/questions/13750/what-are-the-applications-of-hypergraphs ... https://www.youtube.com/watch?v=UwvZn9lm_98