(A) study on the structure and function of networks via statistical inference and latent geometry

Abstract

Many systems of interacting elements have irregular structures beyond lattices. Networks provide the generalized representation for these systems. In this dissertation, we discuss two approaches to understanding the structure and function of networks: statistical inference and latent geometry. Specifically, we provide three main chapters after the introduction in Chapter 1. In Chapter 2, we discuss how the inference of network models provides insights into the generative mechanisms of networks with an application of the stochastic block model to synergy networks of scientists. In Chapter 3, we discuss the inference of the latent geometric models for real-world multiplex networks and its relation to robustness. In Chapter 4, we further discuss the robustness of multiplex networks from the perspective of percolation transitions. The implications of our works are twofold. First, an inferential approach can distinguish randomness and organizational principles in the structure of networked systems. Second, a latent geometric approach reveals the interplay between the structure and function of complex networks by treating them as effective low-dimensional systems.