On Steiner Centers and Steiner Medians of Graphs

Because vertices most central with respect to the center (minimax distance) criterion and the median (minisum distance) criterion can be arbitrarily far apart even in trees, several sequences of central sets have been introduced. Each such sequence is based on an underlying concept that shows the center and median to be part of a spectrum of centrality measures, and several such sequences are examined. The difference between the median criterion and the centroid (maximin voting) criterion is also described, and a centroid-to-median sequence is defined for arbitrary graphs. © 1999 John Wiley & Sons, Inc. Networks 34:244-249,1999