ClosenessCentrality

How close a vertex of a Graph is, on average, to every other vertex it can reach.

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguageClosenessCentrality✓↗

ClosenessCentrality(g)every vertex's closeness centrality, in VertexList(g) order.

ClosenessCentrality(g, v)just v's closeness centrality.

Typed signatures

Type	Package	Applies
(value, any?) -> list<number> | number	combinatorics	always

Domain: Collections

Details

• Defined as (r - 1) / (sum of distances from v to those r - 1 vertices), where r is the number of vertices reachable from v INCLUDING v itself -- restricting to the reachable set rather than treating a disconnected graph as an error. 0 for a vertex with nothing reachable.
• Distances respect edge direction, same as GraphDistance (out-distances from v). Kernel-unverified against a live Wolfram session -- see the PR notes for the exact formula chosen.

Examples

Basic #

live ↗

In$\mathrm{ClosenessCentrality}(\mathrm{StarGraph}(5), 1)$Out$1$

Applications #

live ↗

In$\mathrm{Reverse}(\mathrm{SortBy}(\bigl\lbrack\mathrm{VertexList}(g), \mathrm{ClosenessCentrality}(g)\bigr\rbrack^T, \mathrm{Last}))$Out$\bigl\lbrack\mathrm{ClosenessCentrality}(g), \mathrm{VertexList}(g)\bigr\rbrack$

About

Examples	2
Checked against	Wolfram Language 1 agree1 unevaluated
Crosswalk	Wolfram Language

See also: EigenvectorCentrality, GraphDistance