Topology in Complex Networks: Insights from Topological Data Analysis

This lecture explores the role of higher-order topological properties in the functionality of complex networks. It introduces topological data analysis (TDA) as a methodology to infer geometric and topological structures directly from data, enhancing our understanding of complex systems. The lecture covers the use of TDA for structural break detection and price anomaly detection in time series and dynamic networks. It delves into the concept of persistent homology, which studies data shape through a multi-resolution view of nested simplicial complexes. The application of TDA in Ethereum blockchain networks is also discussed, focusing on anomaly detection and price forecasting. Collaborative research efforts and future directions in statistical inference for TDA are highlighted.