06.11.2023 (Monday)

PR KCL Probability Seminar: When is a critical Random intersection graph different from a Erdos-Renyi one?

regular seminar Minmin Wang (University of Sussex)

at:
15:00 - 16:00
KCL, Strand
room: S4.29
abstract:

Random intersection graph is a simple random graph model that incorporates community structures. To build such a graph, imagine there are n individuals and m potential communities, where each individual joins a community independently with probability p. Two individuals are adjacent to each other in the random intersection graph G(n, m, p) if and only if they belong to a common community. It is known that if m>>n^3, then the model is asymptotically equivalent to an Erdos-Renyi graph G(n, q) with a suitable q. I’ll discuss other ways to compare the two models, particularly regarding the scaling limit of the graphs inside the critical window and number of triangles found in the large components.

Keywords: