Graph center

Equivalently, it is the set of vertices with eccentricity equal to the graph's radius.

Finding the center of a graph is useful in facility location problems where the goal is to minimize the worst-case distance to the facility.

For example, placing a hospital at a central point reduces the longest distance the ambulance has to travel.

[4][5] Another algorithm has been proposed based on matrix calculus.

[6] The concept of the center of a graph is related to the closeness centrality measure in social network analysis, which is the reciprocal of the mean of the distances d(A,B).

A graph with central points colored red. These are the three vertices A such that d ( A , B ) ≤ 3 for all vertices B . Each black vertex is a distance of at least 4 from some other vertex.