View source for Link (geometry)

In [[geometry]], the '''link''' of a vertex of a [[Two-dimensional space|two-dimensional]] [[simplicial complex]] is a [[Graph (mathematics)|graph]] that encodes information about the local structure of the complex at the [[Vertex (geometry)|vertex]].

== Example ==

The link of a vertex of a tetrahedron is a triangle -- the three vertices of the link corresponds to the three edges incident to the vertex, and the three edges of the link correspond to the faces incident to the vertex.

In this example, the link can be visualized by cutting off the vertex with a plane; formally, intersecting the tetrahedron with a plane near the vertex -- the resulting cross-section is the link.

== Analog to sphere centered a point ==

A link is a graph-theoretic analog to a sphere centered at a point.

== See also ==

* [[Geometry]]
* [[Graph (mathematics)]]
* [[Graph theory]]
* [[Simplicial complex]]
* [[Two-dimensional space]]
* [[Vertex (geometry)]]

== External links == 

* [https://en.wikipedia.org/wiki/Link_(geometry) Link (geometry)] @ Wikipedia