gives the length of the longest shortest path from the source s to every other vertex in the graph g.
uses rules vw to specify the graph g.
Details and Options
- VertexEccentricity is also known as node eccentricity.
- VertexEccentricity[g,s] gives the vertex eccentricity for the connected component in which s is contained.
- The following options can be given:
EdgeWeight Automatic weight for each edge Method Automatic method to use
- Possible Method settings include "BellmanFord" and "Dijkstra".
Examplesopen allclose all
In an PetersenGraph, every vertex has the same eccentricity:
Compute and highlight the vertex eccentricity for special graphs, including GridGraph:
Properties & Relations (3)
In a connected graph, the vertex eccentricity is related to GraphDistance:
The vertex eccentricity in a connected graph is related to GraphDiameter:
For a CompleteGraph, every vertex has eccentricity 1:
The eccentricity path in a PathGraph switches halfway through:
In a WheelGraph of size 5 or more, the eccentricity is 1 at the hub and 2 elsewhere:
In a GridGraph, the eccentricity path always ends in a corner of the grid:
In a CompleteKaryTree, the eccentricity path always ends in a leaf:
Wolfram Research (2010), VertexEccentricity, Wolfram Language function, https://reference.wolfram.com/language/ref/VertexEccentricity.html (updated 2015).
Wolfram Language. 2010. "VertexEccentricity." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/VertexEccentricity.html.
Wolfram Language. (2010). VertexEccentricity. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/VertexEccentricity.html