The continuous center set of a network

The continuous radius of a network N is the minimum for all points of N (i.e., vertices or points on edges) of the maximum distance from x to any other point y of N.Any point of N remote from any other point of a distance not exceeding the continuous radius is a continuous center. The continuous center set of N is the union of all continuous centers.Properties of the continuous center set are studied and an algorithm is given to determine it, which requires O(m2log m) time and O(m) space in the worst case, m being the number of edges of N.