Fig. 3

Matchings of a similarity graph and their respective weighted relational diagrams. Considering the same genomes \(A=\{\,[\,\mathtt{1}\,\,\mathtt{2}\,\,\mathtt{3}\,\,\mathtt{4}\,\,\mathtt{5}\,]\,\}\) and \(B=\{\,[\,\mathtt{6}\,\,\overline{\mathtt{7}}\,\,\overline{\mathtt{8}}\,\,\overline{\mathtt{9}}\,\,\mathtt{10}\,\,\mathtt{11}\,]\,\}\) as in Fig. 2, let \(M_1\) (red) and \(M_2\) (blue) be two distinct maximal matchings in \({\mathcal {S}}_{0.1}(A,B)\). We also represent the non-maximal matching \(M_3\) (green) that is a subset of \(M_2\). In the middle part we show diagrams \(WR(A^{M_1},B^{M_1})\) and \(WR(A^{M_2},B^{M_2})\), both with two \(AB\)-paths and two \(AB\)-cycles. In the lower part we show diagrams \(WR(A^{M_\emptyset },B^{M_\emptyset })\), corresponding to the trivial empty matching \(M_\emptyset\) and with two linear singletons (one \(AA\)-path and one \(BB\)-path), and \(WR(A^{M_3},B^{M_3})\), with two \(AB\)-paths and two \(AB\)-cycles. The labeling \((\mathtt{X:Y})\) indicates that \(\mathtt{Y}=s(\mathtt{X},M_i)\)