Van Iersel, Moulton, and Murakami (2020) proved that a level-2 binary phylogenetic network can be uniquely reconstructed based on the matrix of mulitsets of the distances of the leaves. Using a handful of lemma’s each
describing the steps of identifying cherries, uncontained leaves and blobs in the network, I created an algorithm for deconstruction the theoretical network corresponding to the matrix, and constructing the network based on the deconstruction steps. Unfortunately, this algorithm is not of polynomial time, as in the deconstruction programs are run that take time proportional to the sizes of the multisets of distances, which are upperbounded by 4n, where n is the number of leaves in the network. This algorithm is tested on more than 35000 networks with 10 to 24 leaves, and resulted in no errors.