Testing-Based Community Detection Methods for Complex Networks

Community detection is an exploratory method of grouping strongly connected nodes in a network, in most cases using only the network edge structure as a guide. Using discovered communities for downstream analyses can be crucial for real-world decision-making and inference. Recent approaches to community detection include testing-based community extraction, a process in which communities are refined one-by-one via analysis of graph statistics. However, to date, testing-based extraction methods are tied to the configuration model as a null, which applies only to single-layer, binary graphs. In this thesis, testing-based extraction is generalized to arbitrary networks types with a framework called Node-Set Testing (NST). The NST framework defines the broader statistical elements of an approach that uses hypothesis testing to detect communities in complex networks. The NST framework is applied to (i) weighted networks and (ii) bipartite correlation networks, resulting in novel community detection algorithms. In particular, new null models and test statistics are specified to apply iterative hypothesis-testing algorithms on these types of networks. Detailed analyses of the empirical and theoretical properties of the proposed methods are provided. Other chapters in this thesis, while not explicitly involving testing-based algorithms, support the discussion of community detection in heterogeneous networks. One chapter provides a consistency analysis of a significance-based score for community extraction in multilayer networks. In another chapter, preceding the discussion of the NST method for bipartite correlation networks, an application area called eQTL analysis is discussed. In particular, a new model for estimating the effect size and regression correlation of the links in an eQTL network is introduced and studied.Doctor of Philosoph