Many kinds and subclasses of phylogenetic networks have been defined based on the biological phenomenon they represent or which data they are built from (hybridization networks, usually built from rooted trees, recombination networks from binary sequences, median networks from a set of splits, optimal realizations and reticulograms from a distance matrix), or restrictions to get computationally tractable problems (galled trees, and their generalizations level-k phylogenetic networks, tree-child or tree-sibling phylogenetic networks).
D. H. Huson and D. Bryant, Application of Phylogenetic Networks in Evolutionary Studies, Mol. Biol. Evol., 23(2):254-267, 2006.|
Makarenkov, V., Kevorkov, D. and Legendre, P. (2006), Phylogenetic Network Reconstruction Approaches, Applied Mycology and Biotechnology, International Elsevier Series, vol. 6. Bioinformatics, 61-97.