Reach Centrality: Difference between revisions
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(Created page with "{{DISPLAYTITLE: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 $w$. == Related Problems == Subproblem: Directed All-Nodes Reach Centrality, Undirected All-Nodes Reach Centrality, Approximate Reach Centrality Related: Eccentricity, All-Nodes Median Parity, Between...") |
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== 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 $w$.
Related Problems
Subproblem: Directed All-Nodes Reach Centrality, Undirected All-Nodes Reach Centrality, Approximate 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, Undirected 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 TO Problem
| Problem | Implication | Year | Citation | Reduction |
|---|---|---|---|---|
| Diameter | 2015 | https://epubs-siam-org.ezproxy.canberra.edu.au/doi/10.1137/1.9781611973730.112, | link | |
| Diameter | if: to-time: $\tilde{O}(T(n,m,M))$ for $n$-node $m$-edge directed graph with integer weights in $(-M,M)$ then: from-time: $\tilde{O}(T(n,m,M))$ for $n$-node $m$-edge directed graph with integer weights in $(-M,M)$ |
2015 | https://epubs-siam-org.ezproxy.canberra.edu.au/doi/10.1137/1.9781611973730.112, Lemma 3.2 | link |
| Positive Betweenness Centrality | if: to-time: $\tilde{O}(T(n,m))$ for $n$-node $m$-edge directed (resp. undirected) graph then: from-time: $\tilde{O}(T(n,m))$ for $n$-node $m$-edge directed (resp. undirected) graph |
2015 | https://epubs-siam-org.ezproxy.canberra.edu.au/doi/10.1137/1.9781611973730.112, Lemma 4.3 | link |
Reductions FROM Problem
| Problem | Implication | Year | Citation | Reduction |
|---|---|---|---|---|
| Diameter | if: to-time: $\tilde{O}(T(n,m))$ for $n$-node $m$-edge directed (resp. undirected) graph then: from-time: $\tilde{O}(T(n,m))$ for $n$-node $m$-edge directed (resp. undirected) graph |
2015 | https://epubs-siam-org.ezproxy.canberra.edu.au/doi/10.1137/1.9781611973730.112, Lemma 3.1 | link |