Exchangeability and Network Statistics

This lecture covers the concept of exchangeability in statistical analysis of network data, exploring the definition of exchangeable arrays and the Aldous Hoover theorem. It also delves into statistical summaries for networks, discussing subgraph counts and the challenges with network summaries. The lecture further examines the invariance issues with network statistics, the scaling of XF(G) with edge probability, and the asymptotic Gaussian distribution of XF(G) for strictly balanced graphs. Additionally, it presents the average degree and maximum average degree definitions, the concept of strictly balanced graphs, and the Poisson Limit theorem. The lecture concludes with discussions on induced copies, Stochastic blockmodels, and the functional t(F, G) for graph homomorphisms.