The network theory became widely used for Bibliometrics and Scientometrics because it helps in the understanding and interpretation of data resulting from these studies. This article covers a brief history of networks and comments from the random model of Erdós and Rényi to most current models. It presents the most important measures for co-author networks, such as density and centrality measures. It also describes applied empirical research on networks of co-authorship and its findings, as the preferential attachment, cluster property and scale free model. The article concludes that the understanding of the network theory is crucial to the study of the phenomenon of co-authorship and that researchers interested in the subject should expand the use of this theory in their research.