Brunnian link
![This four-component link is a Brunnian link.](/Images/godic/202501/02/Brunnian-4loops.svg0543.png")
![The Borromean rings are the simplest Brunnian link.](/Images/godic/202501/02/BorromeanRings.svg0543.png")
![](/Images/godic/202501/02/Brunnian-3-not-Borromean.svg0543.png")
![](/Images/godic/202501/02/Three-triang-18crossings-Brunnian.svg0543.png")
In knot theory, a branch of topology, a Brunnian link is a nontrivial link that becomes a set of trivial unlinked circles if any one component is removed. In other words, cutting any loop frees all the other loops (so that no two loops can be directly linked).