# degreeVertex -- returns the degree of a vertex

## Synopsis

• Usage:
d = degreeVertex(H,n)
d = degreeVertex(H,V)
• Inputs:
• H, ,
• n, an integer, the index of a vertex
• V, , a vertex/variable of the HyperGraph
• Outputs:
• d, an integer, the degree of vertex V (or vertex number n)

## Description

The degree of a vertex in a (hyper)graph is the number of edges that contain the vertex. In a graph, the degree is also the number of elements in the neighbor set of a vertex.

 i1 : S = QQ[a,b,c,d,e]; i2 : k5 = completeGraph S o2 = Graph{edges => {{a, b}, {a, c}, {a, d}, {a, e}, {b, c}, {b, d}, {b, e}, {c, d}, {c, e}, {d, e}}} ring => S vertices => {a, b, c, d, e} o2 : Graph i3 : dv = degreeVertex(k5,a) o3 = 4 i4 : n = neighbors(k5,a) o4 = {b, c, d, e} o4 : List i5 : #n == dv o5 = true i6 : degreeVertex(k5,2) o6 = 4 i7 : h = hyperGraph {a*b*c,c*d,a*d*e,b*e,c*e} o7 = HyperGraph{edges => {{a, b, c}, {c, d}, {b, e}, {c, e}, {a, d, e}}} ring => S vertices => {a, b, c, d, e} o7 : HyperGraph i8 : degreeVertex(h,a) o8 = 2 i9 : degreeVertex(h,2) -- degree of c o9 = 3