The choice of a measure for structure depends on what is to be conveyed to a particular audience. The algorithm will try to do its best to fit the empirical distances into the space of the permissible target locations of the model which is described by .
There is a large number of centrality concepts readily available, which describe with statistics what people intuitively look for when they visually inspect graphical representations of network data.
A simple concept is Freeman's degree of centrality, based on the rows of the adjacency matrix. His concept of closeness, which evaluates centrality on the basis of the matrix of geodesics, is more informative, additionally taking the shortest indirect distances into account (Freeman (1979)).
Regarding measures of centrality there is a particularly intense discussion of how these indices relate to the concept 'social power', and there exist advanced formal concepts how to approach this theoretical problem methodologically. (Bonnacich (1987) or Friedkin (1991)).