A median of a sequence π=x1,x2,…,xk of elements of a finite metric space (X,d) is an element x for which is minimum. The function M with domain the set of all finite sequences on X and defined by M(π)={x:x is a median of π} is called the median function on X, and is one of the most studied consensus functions. Based on previous characterizations of median sets M(π), a generalization of the median function is introduced and studied on various graphs and ordered sets. In addition, new results are presented for median graphs.

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doi.org/10.1016/j.dam.2006.04.023, hdl.handle.net/1765/19259
Econometric Institute Reprint Series
Discrete Applied Mathematics
Erasmus School of Economics

McMorris, F. R., Mulder, M., & Powers, R. (2006). The t-median function on graphs. Discrete Applied Mathematics, 154(18), 2599–2608. doi:10.1016/j.dam.2006.04.023