The first part of this dissertation introduces a statistical mechanics based formalism to model real-world social networks, while the second, more exploratory part describes application of the network-based description of complex systems in biology where we use boolean networks to model molecular pathway controlling mammal vertebra formation. Although large-scale social networks have a random appearance when naively represented by simple layout/drawing methods, a more careful, statistical analysis of their graph theoretical properties reveals features that are inherent in the formation and evolution of these networks due to human social behavior. In particular, social networks have the empirically observed property of assortativity by degree: a given individual is more likely to be connected to another individual with a similar number of contacts than expected by a uniformly random distribution of the connections. Here we present a dynamic agent-based model of social network evolution that offers an explanation of the observed positive degree assortativity in social networks in terms of a simple mechanism of preference for reciprocity in communication flows: agents drop relationships in which they invest more than their partners and attempt to search and keep relationships in which they invest as much or less. The model rules are built using the Jaynes' Maximum Entropy Principle of statistical mechanics, and the networks are evolved using a standard Monte-Carlo simulation with Metropolis rates. The simulated network properties are compared with those obtained from real cell-phone trace logs (from a non-US based company) among approximately 7 million users over a period of 65 days. Interestingly, not only the assortativity values of the model networks are found to closely match those of the empirical data network, but also many other graph theoretical measures, implying that reciprocity is a major behavioral determinant of social networks. Methods of network theory also have important implications in biology, in the second part of the thesis we develop the boolean network approach to study somite formation. The development of an embryo requires precise spatial and temporal control. During somite formation, the periodic expression of the cyclic genes of the Notch pathway matches the regular formation of somites. It is believed that transcriptional and translational delays drive the oscillatory behavior of the cyclic genes (Hes1/7, Lfng, Mesp2 and Dll) during somite formation. We hypothesize that the delays do not cause the cyclic expression of Hes1/7, Lfng, Mesp2 and Dll in the Notch pathway, but rather, the interaction map of Notch pathway components drives the oscillations during somitogenesis. To investigate this, we construct and analyze two qualitative and logical-based network models, with and without delays, to study the cyclic oscillation of the Hes1/7, Lfng, Mesp2 and Dll during somitogenesis. Our analysis shows that the Notch pathway interaction map could alone determine cyclic expressions on Hes 1/7, L-fng, Mesp2 and Dll. We have also shown that the presence of the delays coordinates the timing of the molecular interactions making them robust. In other words, we have shown that the structure of the network intrinsically determines oscillations but presence of delays stabilizes this behavior in the Notch pathway during somitogenesis.