Eulerian Magnitude Homology - Subgraph Structure and Random Graphs

Explore the connection between graph magnitude homology group ranks and subgraph structure in this 47-minute talk by Giuliamaria Menara. Delve into the concepts of eulerian magnitude homology and discriminant magnitude homology, introduced in collaboration with Chad Giusti. Examine the relationship between eulerian magnitude homology group ranks on the first diagonal and specific subgraph class counts. Investigate the limiting behavior of eulerian magnitude homology groups for Erdos-Renyi random graphs and random geometric graphs, uncovering vanishing thresholds and characterizing magnitude homology group generators. Gain insights into the asymptotic estimate of expected eulerian magnitude homology rank along the first diagonal for these random graph models.