A first attempt to give an arithmetic description of the ugraph with weights is by a horizontal list of nodes and weights: 
  1 (2000)    2 (2500)    3 (7500)      4 (1700)
and a horizontal listing of edges and weights: 
  1-2 (10)    1-3 (25)    2-3 (12)    2-4 (30)    3-4 (13)
The short form (see additional materal for chapter01) of the adjacency array with weights is 
 S  1,2,3,(2000,10,25)