Undirected All-Nodes Reach Centrality: Difference between revisions
(Created page with "{{DISPLAYTITLE:Undirected All-Nodes Reach Centrality (Vertex Centrality)}} == Description == The reach centrality of a node $w$ is the smallest distance $r$ such that any $s-t$ shortest path passing through $w$ has either $s$ or $t$ in the ball of radius $r$ around $w$. Undirected All-Nodes Reach Centrality is the version of the problem in an undirected graph where you must calculate the reach centrality of each node. == Related Problems == Generalizations: Reach...") |
No edit summary |
||
| Line 14: | Line 14: | ||
== Parameters == | == Parameters == | ||
n: number of vertices | |||
m: number of edges | |||
m: number of edges | |||
== Table of Algorithms == | == Table of Algorithms == | ||
Revision as of 12:04, 15 February 2023
Description
The reach centrality of a node $w$ is the smallest distance $r$ such that any $s-t$ shortest path passing through $w$ has either $s$ or $t$ in the ball of radius $r$ around $w$.
Undirected All-Nodes Reach Centrality is the version of the problem in an undirected graph where you must calculate the reach centrality of each node.
Related Problems
Generalizations: Reach Centrality
Related: Eccentricity, All-Nodes Median Parity, Betweenness Centrality, Approximate Betweenness Centrality, Positive Betweenness Centrality, Directed All-Nodes Positive Betweenness Centrality, Undirected All-Nodes Positive Betweenness Centrality, Directed All-Nodes Reach Centrality, Approximate Reach Centrality
Parameters
n: number of vertices
m: number of edges
Table of Algorithms
Currently no algorithms in our database for the given problem.
Reductions FROM Problem
| Problem | Implication | Year | Citation | Reduction |
|---|---|---|---|---|
| Undirected, Weighted APSP | if: to-time: Truly subcubic then: from-time: Truly subcubic |
2015 | https://epubs-siam-org.ezproxy.canberra.edu.au/doi/10.1137/1.9781611973730.112, Corollary 4.1 | link |