Social Network, Exploring Dynamic Network Evolution From Triadic Closures to Block-Structured Networks
In this dissertation, we embark on a comprehensive exploration of dynamic network evolution within a triadic closure framework. Furthermore, we extend this model’s applicability to encompass more intricate scenarios, including networks with block structures—such as the dynamics of interpersonal connections between two distinct schools within a town. Our investigation encompasses an analysis of fundamental network properties and the consequential implications for their evolutionary trajectories.
Network science stands as a pivotal field of inquiry, specializing in the scrutiny of the topological structures, dynamics, and functionalities of complex networks. This interdisciplinary domain equips researchers with versatile tools applicable across an array of systems, ranging from social networks to biological networks. Its multidisciplinary nature draws upon mathematical principles, computer science methodologies, sociological insights, and insights from various allied fields. Within the context of this dissertation, we introduce a specialized stochastic dynamical system tailored to elucidate the dynamics of friendship between two schools. We harness the power of mean field theory to investigate the stability of this system.
Throughout the course of this research endeavor, we delve into the intricate interplay of parameter values and their role in steering the network’s evolution. As detailed in Section \ref{1_c}, our utilization of the mean field approach empowers us to precisely compute quasi-stable states and approximate numerical simulations within networks featuring a single community. Additionally, we adapt this methodology to estimate parameters within multi-community networks, albeit with a slightly reduced degree of precision. In Section \ref{3}, we introduce innovative techniques for community detection and maximum likelihood estimation. These techniques are founded on the principles of the triadic closure mechanism and the Markov model, enabling us to fit social network data with remarkable accuracy.
This dissertation represents a rigorous exploration of dynamic network evolution, with a specific focus on the triadic closure framework and its extension to block-structured networks. It underscores the paramount importance of network science as a multifaceted discipline that offers invaluable tools for deciphering the complexities of diverse systems. Our utilization of mean field theory, coupled with innovative parameter estimation techniques, positions this research at the forefront of network science, offering fresh insights into the intricate dynamics of evolving networks.
