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.

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).

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.

$\mathrm{with}\left(\mathrm{GraphTheory}\right)\:$

$G≔\mathrm{Graph}\left(\left[1\,2\,3\,4\,5\,6\right]\,\left\{\left\{1\,3\right\}\,\left\{1\,6\right\}\,\left\{2\,4\right\}\,\left\{2\,6\right\}\,\left\{3\,6\right\}\,\left\{4\,5\right\}\,\left\{4\,6\right\}\,\left\{5\,6\right\}\right\}\right)$

$G≔\mathrm{Graph\; 1:\; an\; undirected\; unweighted\; graph\; with\; 6\; vertices\; and\; 8\; edge(s)}$

$\mathrm{DMrawGraph}\left(G\right)$

$\mathrm{DMrawGraph}\left(\mathrm{Graph\; 1:\; an\; undirected\; unweighted\; graph\; with\; 6\; vertices\; and\; 8\; edge(s)}\right)$

$\mathrm{Eccentricity}\left(G\,6\right)$

$1$

$\mathrm{Eccentricity}\left(G\right)$

$\left[2\,2\,2\,2\,2\,1\right]$

$H≔\mathrm{Graph}\left(\left[a\,b\,c\,d\right]\,\left\{\left\{a\,b\right\}\,\left\{a\,d\right\}\,\left\{b\,c\right\}\,\left\{c\,d\right\}\right\}\right)$

$H≔\mathrm{Graph\; 2:\; an\; undirected\; unweighted\; graph\; with\; 4\; vertices\; and\; 4\; edge(s)}$

$\mathrm{Eccentricity}\left(H\,\mathrm{output}=\mathrm{DataSeries}\right)$

$\left[\begin{array}{cc}a& 2\\ b& 2\\ c& 2\\ d& 2\end{array}\right]$

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

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