Skein (graph theory)

Let ⁠${\displaystyle G}$⁠ be a graph, and ⁠${\displaystyle a}$⁠ and ⁠${\displaystyle b}$⁠ be two distinct vertices of ⁠${\displaystyle G}$⁠. An ⁠${\displaystyle (a,b)}$⁠-skein of strength ⁠${\displaystyle k}$⁠, where ⁠${\displaystyle k}$⁠ is a cardinal number, is then the union of a set of ⁠${\displaystyle k}$⁠ paths joining ⁠${\displaystyle a}$⁠ and ⁠${\displaystyle b}$⁠ such that any two of these paths have only ⁠${\displaystyle a}$⁠ and ⁠${\displaystyle b}$⁠ in common. The skein is then also called a ⁠${\displaystyle k}$⁠-skein.

For a ⁠${\displaystyle k}$⁠-skein in a finite graph, ⁠${\displaystyle k}$⁠ is a natural number.