Graph center
The center (or Jordan center[1]) of a graph is the set of all vertices of minimum eccentricity,[2] that is, the set of all vertices A where the greatest distance d(A,B) to other vertices B is minimal. Equivalently, it is the set of vertices with eccentricity equal to the graph's radius.[3] Thus vertices in the center (central points) minimize the maximal distance from other points in the graph.
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.
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).[1]
[edit] References
- ^ a b Wasserman, Stanley, and Faust, Katherine (1994), Social Network Analysis: Methods and Applications, page 185. Cambridge: Cambridge University Press. ISBN 0521382696
- ^ McHugh, James A., Algorithmic Graph Theory
- ^ Weisstein, Eric W., "Graph center" from MathWorld.
