Assertion: median graph | /r/Desires | median
Facets:
value: to be unique
type: PURPOSE
Source sentences:
text: w k be an arbitrary shortest path that starts and ends within W uv ; then w 2 must also lie within W uv , for otherwise the two points m 1 = m(u,w 1 ,w k ) and m 2 = m(m 1 ,w 2 ...w k ) could be shown (by considering the possible distances between the vertices) to be distinct medians of u, w 1 , and w k , contradicting the definition of a median graph which requires medians to be unique.