This thesis is on the subject of phylogenetic networks. These are schematic
visualisations used mainly to investigate the evolutionary history of species,
but which can be used for any set of distinguishable elements which have diverged from a common ancestor through some evolutionary process. The research specifically focuses on a way to encode these phylogenetic networks, called μ-representation, which enables researchers to efficiently compare networks in polynomial time. The main contribution of this thesis lies in demonstrating that there are certain classes of phylogenetic networks for which the μ-representation or a modified version thereof serves as a unique encoding and can therefore be used to generate a metric for comparison. Additionally, it is shown that these results do not extend to some other classes of networks. Furthermore, this research shows that certain other information can be gained from analysing the μ-representation of a network, such as which nodes are adjacent to so-called bridges or cut-edges, and what the in-degrees of the nodes in the network are.