SHORTEST COXXECTIOX XETWORKS 



1395 



When the construction of shortest connection networks is thus reduced 

 to processes involving only the numerical distance labels on the various 

 possi))le links, the actual location of the points representing the various 

 terminals in a graphical representation of the problem is, of course, 

 inconsequential. The problem of Fig. 4(a) can just as well be represented 

 by Fig. 5(a), for example, and PI and P2 applied to obtain the SCX 

 of Fig. 5(b). The original metric problem concerning a set of points in 

 the plane has now been abstracted into a problem concerning labelled 

 graphs. The correspondence between the terminology employed thus 

 far and more conventional language of Graph Theory is as follows: 



terminal <-^ vertex 



possible link <-^ edge 



length of link <-> "length" (or "weight") of edge 



connection network <-^ spanning subgraph 



(without closed loops) <-^ (spanning subtree) 



(a) 



Fig. 4 — Example of a shortest spanning subtree of a complete labelled graph. 



(D 



® 6.7 % 



8.0 



(a) 



@ 



(b) 



Fig. 5 — Example of a shortest spanning sul)trec of a complcto lal)ellpd grai)h 



