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gives the length of the longest shortest path from the source s to every other vertex in the graph g.
  • VertexEccentricity gives the vertex eccentricity for the connected component in which s is contained.
Find the vertex eccentricity of vertex 1 in a graph:
Find the vertex eccentricity of vertex 1 in a graph:
Click for copyable input
Click for copyable input
VertexEccentricity works with undirected graphs:
Directed graphs:
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 Gilbert random graph:
The Barabasi-Albert random graph:
The de Solla Price random graph:
People at a family gathering:
Use Subsets to create edges between all members of a family:
The resulting social graph:
Low eccentricity indicates close relation to everybody at the gathering. Compare Larry and Rudy:
Build a network of related concepts based on the "See Also" section of reference pages:
These are the "See Also" entries for Graph:
Generate the whole "See Also" graph, with edges directed to the page where the "See Also" item appears:
Use VertexEccentricity to compare importance of concepts—the lower, the more important:
In a connected graph, the vertex eccentricity is related to GraphDistance:
The vertex eccentricity in a connected graph is related to GraphDiameter:
Illustrate 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:
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