Neighbour joining (NJ, paper) is a phylogeny reconstruction method. It differs from UPGMA in the way it computes the distances between clusters. This algorithm first assumes that the phylogeny is a star graph. Then it finds the pair of vertices that when merged and split out gives the minimal total edge length \(S_{ij}\) of the new almost-star graph. (See eq. (4) and figure 2a and 2b in the paper.) \[ S_{i,j} = \frac1{2(n-2)} \sum_{k\not\in \{i,j\}}(d(i, k)+d(j,k)) + \frac 12 d(i,j)+\frac 1{n...
