 Graph eccentricity

For a vertex $v$ of a finite connected graph $G$, its graph eccentricity is the greatest graph distance to any other vertex:The graph radius is the minimum eccentricity and the graph diameter is the maximum. Eccentricity therefore measures the worst travel distance from a chosen starting point, rather than its average travel distance.

In the four-vertex path graph $1-2-3-4$, the eccentricities are $3,2,2,3$. The two middle vertices are best in this worst-case sense; the radius is two and the diameter three. In a star graph with at least two leaves, the central vertex has eccentricity one and every leaf has eccentricity two. For a disconnected graph, distances across components are usually infinite, so a finite-valued eccentricity requires restricting to a component or stating another convention.