At the traditional location problems on networks consider discrete nodal demand. However, accidents may happen at any point in the road. Demand set is the continuum set of all points on a network graph. The issue of general absolute center was studied in this paper. With the assumption that the distance-matrix of the network is available, let | E | be the number of edges of a network. According to the character of the graph of distance function and its graphical nature which reflects the relationship between points and edges, an O(| E |2 ⋅lg | E |) algorithm about the location problem of single emergency service was given, so that emergency service emergency response time of the maximum shortest.