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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
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Options  
WorkingPrecision  
Applications  
Properties & Relations  
See Also
Related Guides
History
Cite this Page

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:

Wolfram Language code: g = ExampleData[{"NetworkGraph", "Friendship"}];
Wolfram Language code: StatusCentrality[g]

Highlight:

Wolfram Language code: HighlightGraph[g, VertexList[g], VertexSize -> Thread[VertexList[g] -> Rescale[%]]]

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

Wolfram Language code: g = ExampleData[{"NetworkGraph", "Friendship"}];
Wolfram Language code: Part[VertexList[g], Ordering[StatusCentrality[g], All, Greater]]

Scope  (6)

StatusCentrality works with undirected graphs:

Wolfram Language code: StatusCentrality[[image]]

Directed graphs:

Wolfram Language code: StatusCentrality[[image]]

Multigraphs:

Wolfram Language code: StatusCentrality[[image]]

Mixed graphs:

Wolfram Language code: StatusCentrality[[image]]

Use rules to specify the graph:

Wolfram Language code: StatusCentrality[{1 -> 3, 2 -> 1, 3 -> 6, 4 -> 6, 1 -> 5, 5 -> 4, 6 -> 1}]

StatusCentrality works with large graphs:

Wolfram Language code: g = RandomGraph[{10000, 10005}];
Wolfram Language code: StatusCentrality[g, WorkingPrecision -> 20]//Shallow//Timing

Options  (3)

WorkingPrecision  (3)

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

Wolfram Language code: StatusCentrality[[image]]

Specify a higher working precision:

Wolfram Language code: StatusCentrality[[image], WorkingPrecision -> 50]

Infinite working precision corresponds to exact computation:

Wolfram Language code: StatusCentrality[[image] , WorkingPrecision -> ∞]

Applications  (1)

Highlight the status centrality for StarGraph:

Wolfram Language code: HighlightCentrality[g_, cc_] := HighlightGraph[g, Table[Style[VertexList[g][[i]], ColorData["TemperatureMap"][cc[[i]] / Max[cc]]], {i, VertexCount[g]}]];
Wolfram Language code: g = StarGraph[8, VertexSize -> Large];
Wolfram Language code: cc = StatusCentrality[g];
Wolfram Language code: HighlightCentrality[g, cc]

GridGraph:

Wolfram Language code: g = GridGraph[{10, 10}, VertexSize -> Large];
Wolfram Language code: cc = StatusCentrality[g];
Wolfram Language code: HighlightCentrality[g, cc]

CompleteKaryTree:

Wolfram Language code: g = CompleteKaryTree[3, 3, VertexSize -> Large];
Wolfram Language code: cc = StatusCentrality[g];
Wolfram Language code: HighlightCentrality[g, cc]

PathGraph:

Wolfram Language code: g = PathGraph[Range[20], VertexSize -> Large];
Wolfram Language code: cc = StatusCentrality[g];
Wolfram Language code: HighlightCentrality[g, cc]

Properties & Relations  (2)

Status centrality for isolated vertices is taken to be zero:

Wolfram Language code: StatusCentrality[[image]]

Use VertexIndex to obtain the centrality of a specific vertex:

Wolfram Language code: g = ExampleData[{"NetworkGraph", "Friendship"}];
Wolfram Language code: StatusCentrality[g][[VertexIndex[g, "Anna"]]]
Wolfram Research (2012), StatusCentrality, Wolfram Language function, https://reference.wolfram.com/language/ref/StatusCentrality.html (updated 2015).

Text

Wolfram Research (2012), StatusCentrality, Wolfram Language function, https://reference.wolfram.com/language/ref/StatusCentrality.html (updated 2015).

CMS

Wolfram Language. 2012. "StatusCentrality." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/StatusCentrality.html.

APA

Wolfram Language. (2012). StatusCentrality. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/StatusCentrality.html

BibTeX

@misc{reference.wolfram_2026_statuscentrality, author="Wolfram Research", title="{StatusCentrality}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/StatusCentrality.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_statuscentrality, organization={Wolfram Research}, title={StatusCentrality}, year={2015}, url={https://reference.wolfram.com/language/ref/StatusCentrality.html}, note=[Accessed: 13-June-2026]}