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A classical result in phylogenetic trees is that a binary phylogenetic tree adhering to the molecular clock hypothesis exists if and only if the matrix of distances between taxa is ultrametric. The ultrametric condition is very restrictive. In this paper, we study phylogenetic networks that can be constructed assuming the molecular clock hypothesis. We characterize distance matrices that admit such networks for three and four taxa. We also design two algorithms for constructing networks optimizing the least-squares fit.