  Gomory-Hu tree [Gomory and Hu, 1961] is a succinct representation of pairwise
minimum cuts in an undirected graph. When the input graph has general edge
weights, classic algorithms need at least cubic running time to compute a
Gomory-Hu tree. Very recently, the authors of [AKL+, arXiv v1, 2021] have
improved the running time to $\tilde{O}(n^{2.875})$ which breaks the cubic
barrier for the first time. In this paper, we refine their approach and improve
the running time to $\tilde{O}(n^2)$. This quadratic upper bound is also
obtained independently in an updated version by the same group of authors
[AKL+, arXiv v2, 2021].
