The preferential attachment model is a natural and popular random graph model for a growing network that contains very well-connected ``hubs''. Despite intense interest in the higher-order connectivity of these networks, their Betti numbers at higher dimensions have been largely unexplored.
In this talk, after a brief survey on random topology, we study the clique complexes of preferential attachment graphs, and we prove the asymptotics of the expected Betti numbers. If time allows, we will briefly discuss their homotopy connectedness as well. This is joint work with Gennady Samorodnitsky, Christina Lee Yu and Rongyi He, and it is based on the preprint https://arxiv.org/abs/2305.11259
Further Information
Chunyin Siu (Alex) is a PhD candidate at Cornell University at the Center for Applied Mathematics, and is a Croucher scholar (2019) and a Youde scholar (2018).
His primary research interests lie in the intersection of topological data analysis, network analysis, topological statistics and computational geometry. He is advised by Prof. Gennady Samorodnitsky. Before coming to Cornell University, he was a MPhil. student advised by Prof. Ronald (Lokming) Lui at the Chinese University of Hong Kong.