Fig. 3

Example of a network N (left) with a linear order \(\sigma \) of its nodes (below) as well as their canonical tree \(\Gamma ^\sigma \) (right) whose arcs are not drawn (the arcs of N are drawn in their stead). Reticulations are black, leaves are boxes. For the first (wrt. \(\sigma \)) reticulation x, the set \(V(\Gamma ^\sigma _x)\) is marked (gray area) and equals \(\sigma [1..x]\) in this example. Further, the arcs in \( {A}_{x}{(N)}\) are dotted and the nodes in \(\hbox {YW}_{x}^{\Gamma }=\hbox {ZW}_{x}^{\sigma }\) are gray pentagons. Note that \({x\mathop {\leadsto }\limits ^{N,\sigma } \rho _N}\) but neither \({\rho _N\mathop {\leadsto }\limits ^{N,\sigma } x}\) (since \(x\notin \sigma [1..\rho _N]\)) nor \({z\mathop {\leadsto }\limits ^{N,\sigma } x}\) (since x is not weakly connected to z in \(N[\sigma [1..z]]\))