RadialityCentrality

RadialityCentrality[g]

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

RadialityCentrality[g,"In"]

gives a list of in-centralities for a directed graph g.

RadialityCentrality[g,"Out"]

gives a list of out-centralities for a directed graph g.

RadialityCentrality[{vw,},]

uses rules vw to specify the graph g.

Details

  • Radiality in-centralities are also known as integration centralities.
  • RadialityCentrality will give high centralities to vertices that are a short distance to every other vertex in its reachable neighborhood compared to its diameter.
  • Radiality out-centrality for a vertex is computed using the out component for the vertex and is given by , where is the distance from to in , is the diameter of , and the sum is over the vertices in .
  • Radiality in-centrality for a vertex is computed using the in component for the vertex and is given by , where is the distance from to in , is the diameter of , and the sum is over the vertices in .
  • The radiality centrality for an isolated vertex is taken to be zero.
  • RadialityCentrality works with undirected graphs, directed graphs, weighted graphs, multigraphs, and mixed graphs.

Examples

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Basic Examples  (2)

Compute radiality centralities:

Highlight:

Rank vertices. Highest-ranked vertices are at a short distance to all reachable vertices compared to the highest distance in the graph:

Scope  (8)

RadialityCentrality works with undirected graphs:

Directed graphs:

Weighted graphs:

Multigraphs:

Mixed graphs:

Use rules to specify the graph:

Compute in-centralities and out-centralities:

RadialityCentrality works with large graphs:

Applications  (2)

Rank vertices of a graph by the degree of easiness to reach other vertices:

Highlight the radiality centrality for CycleGraph:

GridGraph:

CompleteKaryTree:

PathGraph:

Properties & Relations  (3)

Radiality centrality is between 0 and 1:

RadialityCentrality can be computed using GraphDistanceMatrix:

Compare:

Use VertexIndex to obtain the centrality of a specific vertex:

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

Text

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

BibTeX

@misc{reference.wolfram_2021_radialitycentrality, author="Wolfram Research", title="{RadialityCentrality}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/RadialityCentrality.html}", note=[Accessed: 01-December-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_radialitycentrality, organization={Wolfram Research}, title={RadialityCentrality}, year={2015}, url={https://reference.wolfram.com/language/ref/RadialityCentrality.html}, note=[Accessed: 01-December-2021 ]}

CMS

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

APA

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