Visualising the evolutionary history of a set of sequences is a challenge for molecular phylogenetics. One approach is to use undirected graphs, such as median networks, to visualise phylogenies where reticulate relationships such as recombination or homoplasy are displayed as cycles. Median networks contain binary representations of sequences as nodes, with edges connecting those sequences differing at one character, hypothetical ancestral nodes are invoked to generate a connected network which contains all most parsimonious trees. Quasi-median networks are a generalisation of median networks which are not restricted to binary data, although phylogenetic information contained within the multistate positions can be lost during the preprocessing of data. Where the history of a set of samples contain frequent homoplasies or recombination events quasi-median networks will have a complex topology. Graph reduction or pruning methods have been used to reduce network complexity but some of these methods are inapplicable to datasets in which recombination has occurred and others are procedurally complex and/or result in disconnected networks.