Positive Betweenness Centrality (Vertex Centrality)
Jump to navigation
Jump to search
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/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/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/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/doi/10.1137/1.9781611973730.112, Theorem 4.3 | link |