degreeVertex -- returns the degree of a vertex

Usage:

d = degreeVertex(H,n)

d = degreeVertex(H,V)
Inputs:
- H, a hypergraph,
- n, an integer, the index of a vertex
- V, a ring element, 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

Ways to use degreeVertex:

degreeVertex(HyperGraph,RingElement)
degreeVertex(HyperGraph,ZZ)

For the programmer

The object degreeVertex is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/EdgeIdeals.m2:2391:0.

degreeVertex -- returns the degree of a vertex

Description

See also

Ways to use degreeVertex:

For the programmer