Two-Sample Hypothesis Testing for Random Graphs

Hypothesis testing for latent position random graphs is a growing area of research, particularly motivated by needs in areas such as neuroscience, fraud detection, and social networks. We explore two problems of statistical inference. Currently, methods such as adjacency spectral embedding (ASE) are used to create test statistics for random graphs. The first chapter of our study presents non-metric multidimensional scaling as an alternative to ASE. We show our procedure is functional for both simulated data and for graphs generated from MRI scans. In the second chapter we explore classical applications of statistical inference in a multi-graph setting. We will isolate important vertices across a set of graphs, and then determine correlations between the important vertices and physical vertex features. We use the same MRI data from Chapter 1. The overall goal of these studies is to test new concepts of statistical inference on graphs via simulations and explorations of real-world data