Positive Betweenness Centrality: Difference between revisions
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(Created page with "{{DISPLAYTITLE:Positive Betweenness Centrality (Vertex Centrality)}} == Description == Given a graph $G=(V,E)$ and a vertex $v \in V$, determine whether the betweenness centrality of $v$ is positive. == Related Problems == Generalizations: Betweenness Centrality Subproblem: Directed All-Nodes Positive Betweenness Centrality, Undirected All-Nodes Positive Betweenness Centrality Related: Eccentricity, All-Nodes Median Parity, Approximate Betwe...") |
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== Parameters == | == Parameters == | ||
$n$: number of nodes | |||
m: number of edges | |||
$m$: number of edges | |||
== Table of Algorithms == | == Table of Algorithms == | ||
Latest revision as of 07:53, 10 April 2023
Description
Given a graph $G=(V,E)$ and a vertex $v \in V$, determine whether the betweenness centrality of $v$ is positive.
Related Problems
Generalizations: Betweenness Centrality
Subproblem: Directed All-Nodes Positive Betweenness Centrality, Undirected All-Nodes Positive Betweenness Centrality
Related: Eccentricity, All-Nodes Median Parity, Approximate Betweenness Centrality, Undirected All-Nodes Positive Betweenness Centrality, Reach Centrality, Directed All-Nodes Reach Centrality, Undirected All-Nodes Reach Centrality, Approximate Reach Centrality
Parameters
$n$: number of nodes
$m$: 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 | if: to-time: $\tilde{O}(T(n,m,M))$ for $n$-node $m$-edge directed (resp. undirected) graph with integer weights in $(-M,M)$ then: from-time: $\tilde{O}(T(n,m,M))$ for $n$-node $m$-edge directed (resp. undirected) graph with integer weights in $(-M,M)$ |
2015 | https://epubs-siam-org.ezproxy.canberra.edu.au/doi/10.1137/1.9781611973730.112, Lemma 4.2 | 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 4.1 | link |
| Reach 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 |
| CNF-SAT | if: to-time: $O(m^{2-\epsilon})$ for some $\epsilon > {0}$ then: from-time: $O*({2}^{({1}-\delta)n})$ for some $\delta > {0}$ |
2015 | https://epubs-siam-org.ezproxy.canberra.edu.au/doi/10.1137/1.9781611973730.112, Theorem 4.3 | link |