Root-Finding and Opinion Dynamics in Random Growing Networks

Various real-world networked systems of contemporary interest in science and society feature the time-evolution of a complex network through the sequential addition of vertices and edges. Such systems are naturally modeled by temporal networks that grow and evolve over time according to stochastic interaction rules governing the addition of vertices, formation of edges, and variation of vertex states. Developing and analyzing the behavior of these temporal network models is therefore an important research direction with the potential to impact various domains featuring networked systems in science and society. This thesis considers two problems in random growing networks: root-finding in random growing trees and opinion dynamics in co-evolving random networks. In the first setting, we investigate the recovery of the initial vertex of a randomly grown tree based on its final observed undirected structure, resulting in a network archaeology problem. In the second, we introduce a novel model for opinion dynamics in social networks, in which the structure of the network co-evolves with the opinions of its individuals, and examine how local rules governing opinion updates and network evolution in a social network jointly influence the long-term behavior of the global opinion distribution. A unifying theme throughout this work is the use of large-scale numerical experiments to uncover empirical regularities that inform conjectures and guide future theoretical work, providing insight into how local randomness and growth mechanisms shape global network behavior.