Social Network Analysis (SNA) is becoming an important tool to analyze, model, and simulate the behavior of groups of people or entities both on the global level (how two or more groups interact with other group(s)) and on the local level (how individuals interact with each other within the same network.) In the past two decades, SNA has been used to analyze relations and ties among individuals of the same network and similarities between different networks in an attempt to obtain a better understanding on how societies/subsocieties interact. I propose a method to estimate missing edges in a graph using covariate information and similarities among actors, which I called the EMLUCI model. Concurrently, this model can be used to estimate missing nodes in a graph based on the structure of the network by transforming vertices onto the dual space of edges. Then I present a technique to predict the emergence of new actors in a network using stochastic processes. I further apply quantitative methods to examine social networks as a time series to obtain a better understanding on how these networks evolve. Finally, I suggest a model for preferential attachments.