Fig. 1
From: Efficient gene orthology inference via large-scale rearrangements
On the top part is displayed the gene similarity graph \(\mathcal {S}({\mathbb {A}},{\mathbb {B}})\) of genomes \({\mathbb {A}}=\{\;[\;\texttt{1}\;\;\texttt{2}\;\;\texttt{3}\;\;\texttt{4}\;]~[\;\texttt{5}\;\;\overline{\texttt{6}}\;]\;\}\) and \({\mathbb {B}}=\{\;[\;\texttt{7}\;\;\overline{\texttt{8}}\;\;\overline{\texttt{9}}\;\;\overline{\texttt{10}}\;\;\texttt{11}\;\;\texttt{12}\;\;\texttt{13}\;]\;\}\) and next to it a table with the ranking of four distinct ortholog-sets. On the middle the rearrangement scenarios induced by two of these ortholog-sets are shown. On the bottom part the family-free relational graph \(F\!F\!R({\mathbb {A}},{\mathbb {B}},\mathcal {S})\) is illustrated, highlighting the edges of the decomposition corresponding to the (black) ortholog-set \({\mathcal {O}}=\{\{\texttt{1},\texttt{7}\}\), \(\{\texttt{3},\texttt{10}\}, \{\texttt{4},\texttt{9}\}, \{\texttt{5},\texttt{13}\}\}\). (This decomposition has two \({\mathbb {A}}{\mathbb {B}}\)-paths, one \({\mathbb {A}}{\mathbb {A}}\)-path and one cycle.) All extremity and indel edges in \(F\!F\!R({\mathbb {A}},{\mathbb {B}},\mathcal {S})\) are respectively scored and weighted according to \(\mathcal {S}({\mathbb {A}},{\mathbb {B}})\) but the scores and weights of edges not derived from \({\mathcal {O}}\) or \(\widetilde{{\mathcal {O}}}\) are omitted