Sleep staging, the process of assigning labels to epochs of sleep, depending on the stage of sleep they belong, is an arduous, time consuming and error prone process as the initial recordings are quite often polluted by noise from different sources. To properly analyze such data and extract clinical knowledge, noise components must be removed or alleviated. In this paper a pre-processing and subsequent sleep staging pipeline for the sleep analysis of electroencephalographic signals is described. Two novel methods of functional connectivity estimation (Synchronization Likelihood/SL and Relative Wavelet Entropy/RWE) are comparatively investigated for automatic sleep staging through manually pre-processed electroencephalographic recordings. A multi-step process that renders signals suitable for further analysis is initially described. Then, two methods that rely on extracting synchronization features from electroencephalographic recordings to achieve computerized sleep staging are proposed, based on bivariate features which provide a functional overview of the brain network, contrary to most proposed methods that rely on extracting univariate time and frequency features. Annotation of sleep epochs is achieved through the presented feature extraction methods by training classifiers, which are in turn able to accurately classify new epochs. Analysis of data from sleep experiments on a randomized, controlled bed-rest study, which was organized by the European Space Agency and was conducted in the "ENVIHAB" facility of the Institute of Aerospace Medicine at the German Aerospace Center (DLR) in Cologne, Germany attains high accuracy rates, over 90% based on ground truth that resulted from manual sleep staging by two experienced sleep experts. Therefore, it can be concluded that the above feature extraction methods are suitable for semi-automatic sleep staging.