StatusCentrality

StatusCentrality[g]

gives a list of status centralities for the vertices in the graph g.

StatusCentrality[{vw,}]

uses rules vw to specify the graph g.

Details and Options

  • StatusCentrality gives a list of centralities that satisfy c=alpha TemplateBox[{a}, Transpose].c+alpha beta, where is the adjacency matrix of g, is the vector of minimums between the inverse of the largest in- or out-degree of each vertex, and is the vertex in-degree of g.
  • The status centrality for an isolated vertex is taken to be zero.
  • StatusCentrality works with undirected graphs, directed graphs, multigraphs, and mixed graphs.

Examples

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Basic Examples  (2)

Compute status centralities:

Highlight:

Rank vertices. Highest-ranked vertices are connected from other well-connected vertices:

Scope  (6)

StatusCentrality works with undirected graphs:

Directed graphs:

Multigraphs:

Mixed graphs:

Use rules to specify the graph:

StatusCentrality works with large graphs:

Options  (3)

WorkingPrecision  (3)

By default, StatusCentrality finds centralities using machine-precision computations:

Specify a higher working precision:

Infinite working precision corresponds to exact computation:

Applications  (1)

Highlight the status centrality for StarGraph:

GridGraph:

CompleteKaryTree:

PathGraph:

Properties & Relations  (2)

Status centrality for isolated vertices is taken to be zero:

Use VertexIndex to obtain the centrality of a specific vertex:

Introduced in 2012
 (9.0)
 |
Updated in 2014
 (10.0)
2015
 (10.3)