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Phylogenetic networks extend phylogenetic trees to model non-verticalinheritance, by which a lineage inherits material from multiple parents. Thecomputational complexity of estimating phylogenetic networks from genome-widedata with likelihood-based methods limits the size of networks that can behandled. Methods based on pairwise distances could offer faster alternatives.We study here the information that average pairwise distances contain on theunderlying phylogenetic network, by characterizing local and global featuresthat can or cannot be identified. For general networks, we clarify that theroot and edge lengths adjacent to reticulations are not identifiable, and thenfocus on the class of zipped-up semidirected networks. We provide a criterionto swap subgraphs locally, such as 3-cycles, resulting in indistinguishablenetworks. We propose the "distance split tree", which can be constructed frompairwise distances, and prove that it is a refinement of the network's tree ofblobs, capturing the tree-like features of the network. For level-1 networks,this distance split tree is equal to the tree of blobs refined to separatepolytomies from blobs, and we prove that the mixed representation of thenetwork is identifiable. The information loss is localized around 4-cycles, forwhich the placement of the reticulation is unidentifiable. The mixedrepresentation combines split edges for 4-cycles, regular tree and hybrid edgesfrom the semidirected network, and edge parameters that encode all informationidentifiable from average pairwise distances.

Identifiability of local and global features of phylogenetic networks from average distances