GraphTheory - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Discrete Mathematics : Graph Theory : GraphTheory Package : GraphTheory/Eccentricity

GraphTheory

  

Eccentricity

  

compute graph eccentricity

 

Calling Sequence

Parameters

Options

Description

Definition

Examples

Compatibility

Calling Sequence

Eccentricity(G, opts)

Eccentricity(G, v)

Parameters

G

-

graph

v

-

(optional) vertex of G

opts

-

(optional) one or more options as specified below

Options

  

The options argument can contain one or more of the options shown below.

• 

output=Array, DataSeries, list, or Vector.

  

This option specifies an alternate container type for the return value. When output is one of Array, list, or Vector, a container of the named type containing the eccentricities for each vertex is returned. When output is DataSeries, the return value is a DataSeries object whose labels correspond to the graph vertices and whose values are the computed eccentricities for the associated vertices. The default container type is a list.

  

The output option cannot be used when a particular vertex v is specified.

Description

• 

The Eccentricity(G,v) command computes the eccentricity for the vertex v in the graph G.

• 

The Eccentricity(G) command returns a list of the computed eccentricities for each vertex in the graph G, listed in the order in which the vertices appear in the list returned by Vertices(G).

Definition

• 

The eccentricity of a vertex v in a graph G is a number which represents the maximum graph distance between v and any other vertex in the graph.

• 

If G is disconnected, then the eccentricity for every vertex is infinity.

• 

If G is a complete graph, then the eccentricity for every vertex is 1.

• 

The maximum of the eccentricities in G is the diameter of G. The minimum of the eccentricities in G is the radius of G.

Examples

withGraphTheory:

GGraph1,2,3,4,5,6,1,3,1,6,2,4,2,6,3,6,4,5,4,6,5,6

GGraph 1: an undirected unweighted graph with 6 vertices and 8 edge(s)

(1)

DrawGraphG

Compute the eccentricity for vertex 6.

EccentricityG,6

1

(2)

Produce a list of eccentricities for all vertices.

EccentricityG

2,2,2,2,2,1

(3)

Produce a DataSeries with labels corresponding to the named vertices.

HGrapha,b,c,d,a,b,a,d,b,c,c,d

HGraph 2: an undirected unweighted graph with 4 vertices and 4 edge(s)

(4)

EccentricityH,output=DataSeries

a2b2c2d2

(5)

Compatibility

• 

The GraphTheory[Eccentricity] command was introduced in Maple 2017.

• 

For more information on Maple 2017 changes, see Updates in Maple 2017.

See Also

GraphTheory[Diameter]

GraphTheory[Distance]

GraphTheory[Radius]