This paper explains the classical social network analysis and discusses how computer networks effect a shift in constructing social networks. The paper then concentrates on analyzing cognitive aspects of a social network, explaining a simple but scalable approach for modeling a socio-cognitive network. Novel measures using such a socio-cognitive network model are defined and applications of such measures to extract useful information is illustrated on the Enron email dataset. The paper then describes a Dempster-Schafer theory based approach towards modeling a cognitive knowledge network and uses the Enron email dataset to illustrate how the proposed model can be used to capture actors' perceptions in a knowledge network. The paper concludes with a summary of the proposed models and a discussion on new research directions that can arise due to such cognitive analyses of electronic communication data.