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A phylogenetic network is a simplex (or 1-component tree-child) network ifthe child of every reticulation node is a network leaf. Simplex networks are asuperclass of phylogenetic trees and a subclass of tree-child networks.Generalizing the Sackin index to phylogenetic networks, we prove that theexpected Sackin index of a random simplex network is asymptotically$\Omega(n^{7/4})$ in the uniform model.

The Sackin Index of Simplex Networks