This method (Saitou and Nei 1987) is a simplified version of the minimum evolution (ME) method (Rzhetsky and Nei 1992). The ME method uses distance measures that correct for multiple hits at the same sites; it chooses a topology showing the smallest value of the sum of all branches (S) as an estimate of the correct tree. However, construction of an ME tree is time-consuming because, in principle, the S values for all topologies must be evaluated. Because the number of possible topologies (unrooted trees) rapidly increases with the number of taxa, it becomes very difficult to examine all topologies.
In the case of the NJ method, the S value is not computed for all or many topologies, but the examination of different topologies is embedded in the algorithm, so that only one final tree is produced. The algorithm of the NJ method is somewhat complicated and is explained in detail in Nei and Kumar (2000, page 103).
The NJ method produces an unrooted tree because it does not require the assumption of a constant rate of evolution. Finding the root requires an outgroup taxon. In the absence of outgroup taxa, the root is sometimes given at the midpoint of the longest distance connecting two taxa in the tree, which is referred to as mid-point rooting.