The Sackin Index of Simplex Networks

A phylogenetic network is a simplex network if the child of every reticulation node is a network leaf and each tree node has at most one reticulation node as its child. Simplex networks are a superclass of phylogenetic trees and a subclass of tree-child networks. Generalizing the Sackin index to phylogenetic networks, we prove that the expected Sackin index of a random simplex network is asymptotically $$\varTheta (n^{7/4})$$ in the uniform model.