can you find all paths and determine the shorts one

8.6 LABELED AND WEIGHTED GRAPHS A graph G is called a labeled graph if its edges and/or vertices are assigned data of one kind or another. In particular, G is called a weighted graph if each edge e of G is assigned a nonnegative number w(e) called the weight or length of v. Figure 8-12 shows a weighted graph where the weight of each edge is given in the obvious way. The weight (or length) of a path in such a weighted graph G is defined to be the sum of the weights of the edges in the path. One important problem in graph theory is to find a shortest path, that is, a path of minimum weight (length), between any two given vertices. The length of a shortest path between P and Q in Fig. 812 is 14; one such path is The reader can try to find another shortest path. Fig. 8-12