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, 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 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		2015	https://epubs.siam.org/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/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/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/doi/10.1137/1.9781611973730.112, Lemma 3.1	link