Audun Myers (08/28/2024): Understanding Temporal (Hyper)graph Dynamics with Zigzag Persistence

Abstract: Temporal hypergraphs are a powerful tool for modeling complex systems with multi-way interactions and temporal dynamics. However, existing tools for studying temporal hypergraphs do not adequately capture the evolution of their topological structure over time. In this work, we leverage zigzag persistence from Topological Data Analysis (TDA) to study the topological evolution of time-evolving graphs and hypergraphs. We apply our pipeline to both several datasets including cyber security and social network datasets and show how the topological structure of their temporal hypergraph representations can be used to understand the underlying dynamics.