The concepts of the 'center' and the 'median vertex' of a graph are generalized to the 'absolute center' and the 'absolute median' of a weighted graph (a graph with weights attached to its vertices as ...

S. L. Hakimi, Optimum Distribution of Switching Centers in a Communication Network and Some Related Graph Theoretic Problems, Operations Research, Vol. 13, No. 3 (May - Jun., 1965), pp. 462-475 ...