Homology of Graphs and Hypergraphs

Explore the topological structure of graphs and hypergraphs in this comprehensive lecture from the Applied Algebraic Topology Network. Delve into the combinatorial and topological aspects of these mathematical objects, examining graphs as one-dimensional simplicial complexes or metric spaces using shortest path distance. Investigate hypergraphs and their complex group-wise interactions, which lack a simple pairwise metric space representation. Survey recent findings on graph and hypergraph homology, including persistent homology of metric graphs and various notions of hypergraph homology. Gain insights from this talk, which was part of the "Topological Data Analysis - Theory and Applications" workshop supported by the Tutte Institute and Western University.