O-linked glycosylation is an important post-translational modification of mucin-type protein, changes to which are important biomarkers of cancer. For this study of the enzymes of O-glycosylation, we developed a shorthand notation for representing GalNAc-linked oligosaccharides, a method for their graphical interpretation, and a pattern-matching algorithm that generates networks of enzyme-catalysed reactions. Software for generating glycans from the enzyme activities is presented, and is also available online. The degree distributions of the resulting enzyme-reaction networks were found to be Poisson in nature. Simple graph-theoretic measures were used to characterise the resulting reaction networks. From a study of in-silico single-enzyme knockouts of each of 25 enzymes known to be involved in mucin O-glycan biosynthesis, six of them, xcexb2-1,4-galactosyltransferase (xcexb24Gal-T4), four glycosyltransferases and one sulfotransferase, play the dominant role in determining O-glycan heterogeneity. In the absence of xcexb24Gal-T4, all Lewis X, sialyl-Lewis X, Lewis Y and Sda/Cad glycoforms were eliminated, in contrast to knockouts of the N-acetylglucosaminyltransferases, which did not affect the relative abundances of O-glycans expressing these epitopes. A set of 244 experimentally determined mucin-type O-glycans obtained from the literature was used to validate the method, which was able to predict up to 98% of the most common structures obtained from human and engineered CHO cell glycoforms. 