Social networks have received much attention these days. Researchers have developed different methods to study the structure and characteristics of the network topology. Our focus is on spectral analysis of the adjacency matrix of the underlying network. Recent work showed good properties in the adjacency spectral space but there are few theoretical and systematical studies to support their findings. In this dissertation, we conduct an in-depth theoretical study to show the close relationship between algebraic spectral properties of the adjacency matrix and various patterns in a broad range of social networks such as friendship networks, alliance and war networks, and distrusted networks. In our framework, we apply matrix perturbation theory and approxima. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]