In geometry, the link of a vertex of a 2-dimensional simplicial complex is a graph that encodes information about the local structure of the complex at the vertex.
Definition
Let <math>\scriptstyle X</math> be a simplicial complex. The link <math>\scriptstyle\operatorname{Lk}(v,X)</math> of a vertex <math>\scriptstyle v</math> of <math>\scriptstyle X</math> is the graph constructed as follows. The vertices of <math>\scriptstyle\operatorname{Lk}(v,X)</math> correspond to edges of <math>\scriptstyle X</math> which are incident to <math>\scriptstyle v</math>. Two such edges are adjacent in <math>\scriptstyle\operatorname{Lk}(v,X)</math> if they are incident to a common 2-cells at <math>\scriptstyle v</math>. The graph <math>\scriptstyle\operatorname{Lk}(v,X)</math> is often given the topology of a ball of small radius centred at <math>\scriptstyle v</math>.
Examples
To follow.
