Neighbor-Joining Method: "The neighbor-joining method (NJ) is a distance based method (requires a distance matrix) and uses the star decomposition method.
Algorithm
Neighbor-joining is a recursive algorithm. Each step in the recursion consists of the following steps:
1. Based on the current distance matrix calculate a modified distance matrix Q (see below).
2. Find the least distant pair of nodes in Q (= the closest neighbors = the pair with the lowest distance value). Create a new node on the tree joining the two closest nodes: the two nodes are linked by their common ancestral node.
3. Calculate the distance of each of the nodes in the pair to their ancestral node.
4. Calculate the distance of all nodes outside of this pair to their ancestral node.
5. Start the algorithm again, considering the pair of joined neighbors as a single taxon (the terminal nodes are replaced by their ancestral node and the ancestral node is then treated as a terminal node) and using the distances calculated in the previous step.
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