Networks play a ubiquitous and crucial role in our lives and are powerful vehicles for us to perceive the interconnected relationships among agents. Understanding the structure of networks helps reveal the underlying mechanism of how agents interact and how networks affect agents' behaviors and decision-making. In this dissertation, we study the network structure of the equity holding network in China and a fundamental network metric, centrality, which is often used in regression models to study the network effect on outcomes of interest. We further propose a novel supervised network centrality estimation (SuperCENT) methodology that improves upon a widely-used method for network regression with centrality.