Bidirectional best hits

From NMPDR Wiki

The best hit of a particular gene to a target genome is the gene in that genome that represents a best match. The match is bidirectional if the two genes are best hits of each other. A bidirectional best hit represents a very strong similarity between two genes.

More formally, the paper The use of gene clusters to infer functional coupling defines a Bidirectional Best Hit (or BBH) as follows:

Given two genes Xa and Xb from two genomes Ga and Gb, Xa and Xb are called a “bidirectional best hit (BBH)” if and only if recognizable similarity exists between them (in our case, we required fasta3 scores lower than 1.0 × 10−5), there is no gene Zb in Gb that is more similar than Xb is to Xa, and there is no gene Za in Ga that is more similar than Xa is to Xb. Genes (Xa, Ya) from Ga and (Xb, Yb) from Gb form a “pair of close bidirectional best hits (PCBBH)” if and only if Xa and Ya are close, Xb and Yb are close, Xa and Xb are a BBH, and Ya and Yb are a BBH.