Individuals are rarely independent and are deeply embedded in their social contexts, where their actions both shape and are shaped by their networks. This interplay is evident in both online and offline social networks, such as those formed among scholars. To explore the effects of influence within these systems, we model social networks using a mathematical graph. The first part of the dissertation investigates the role of gender in the formation of networks among PhD students and their supervisors. Evidence of homophilic behavior and a glass ceiling is identified through co-authorship data from over 1.3 million authors in computer science. We extract the student-supervisor relationship graph and analyze its properties, introducing mathematical formulations for the glass ceiling and influence inequality. A network formation process is established, integrating three characteristics: a lower entry rate for women, preferential attachment, and homophilic behavior, proving these are sufficient for a glass ceiling to arise. The absence of any of these traits negates the glass ceiling's occurrence. The second part examines opinion evolution in networks, where each node has an initial opinion influenced by its neighbors. We analyze variations of this model to determine the time required for the system to stabilize. For asynchronous networks, we discover unweighted graphs that converge in quadratic time, while unweighted synchronous n
