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

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

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

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)

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)

Directed graphs:

Weighted graphs:

Multigraphs:

Mixed graphs:

Use rules to specify the graph:

Compute in-centralities and out-centralities:

## 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:

Compare:

Use VertexIndex to obtain the centrality of a specific vertex: