RadialityCentrality
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
open allclose allBasic Examples (2)
Scope (8)
RadialityCentrality works with undirected 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:
Properties & Relations (3)
Radiality centrality is between 0 and 1:
RadialityCentrality can be computed using GraphDistanceMatrix:
Use VertexIndex to obtain the centrality of a specific vertex:
Text
Wolfram Research (2012), RadialityCentrality, Wolfram Language function, https://reference.wolfram.com/language/ref/RadialityCentrality.html (updated 2015).
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