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[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
VertexEccentricity works with undirected graphs:
Use rules to specify the graph:
VertexEccentricity works with large graphs:
In an PetersenGraph, every vertex has the same eccentricity:
Some Petersen graphs have different eccentricities for the inner and outer subgraphs:
Compute and highlight the vertex eccentricity for special graphs, including GridGraph:
Package this up as a function:
Many special graphs have constant vertex eccentricity:
A few will have varying eccentricity, where some vertices are more centrally located:
Most random graphs have small eccentricities:
The Barabasi–Albert random graph:
The de Solla Price random graph:
Low eccentricity indicates close relation to everybody at the family gathering. Compare Larry and Rudy:
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:
Illustrate the eccentricity of two vertices in a Petersen graph:
For a CompleteGraph, every vertex has eccentricity 1:
The eccentricity path in a PathGraph switches halfway through:
The eccentricity path in a CycleGraph measures both the GraphDiameter and GraphRadius:
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