22/02/2023, 16:00 — 17:00 — Online
Minmin Wang, University of Sussex
Geometry of a large random intersection graph inside the critical window
Random intersection graph is a simple random graph that incorporates community structures. To build such a graph, imagine there are $n$ individuals and $m$ potential communities. Each individual joins a community independently with probability $p$. The graph $G(n, m, p)$ has $n$ nodes, corresponding to the $n$ individuals. Each pair of these individuals share an edge between them if they belong to a common community. The critical threshold for the emergence of a giant component emerges turns out to be at $p^2 ~ 1/nm$. I’ll discuss some results that can help us to understand what a large $G(n, m, p)$ looks like at the critical threshold.
