One important problem in a network G is to locate an (invisible) moving entity by using distance-detectors placed at strategical locations in G. For instance, the famous metric dimension of a graph G is the minimum number k of detectors placed in some vertices {v1,⋯,vk} such that the vector (d1,⋯,dk) of the distances d(vi,r) between the detectors and the entity's location r allows to uniquely determine r for every r∈V(G). In a more realistic setting, each device does not get the exact distance to the entity's location. Rather, given locating devices placed in {v1,⋯,vk}, we get only relative distances between the moving entity's location r and the devices (roughly, for every 1≤i,j≤k, it is provided whether d(vi,r)>, <, or = to d(vj,r)). The centroidal dimension of a graph G is the minimum number of devices required to locate the entity, in one step, in this setting.