The graph radius of a finite connected graph is the least graph eccentricity of any vertex:It is the smallest worst-case travel distance achievable by choosing one starting vertex. The vertices achieving it form the center of a graph.
For the five-vertex path graph, the eccentricities are , so the radius is two and the graph diameter is four. Every finite connected graph satisfies : choose a central vertex and apply the triangle inequality . In a five-cycle every vertex has eccentricity two, so radius and diameter coincide. A vertex minimizing the sum of distances solves a different optimization problem.
New to topics? Read the docs here!