summary in weighted graphedges have an associated number called the weightwhich might represent distancescoststimesor other quantities the minimum spanning tree in weighted graph minimizes the weights of the edges necessary to connect all the vertices an algorithm using priority queue can be used to find the minimum spanning tree of weighted graph the minimum spanning tree of weighted graph models real-world situations such as installing utility cables between cities the shortest-path problem in non-weighted graph involves finding the minimum number of edges between two vertices solving the shortest-path problem for weighted graphs yields the path with the minimum total edge weight the shortest-path problem for weighted graphs can be solved with dijkstra' algorithm the algorithms for largesparse graphs generally run much faster if the adjacency-list representation of the graph is used rather than the adjacency matrix the all-pairs shortest-path problem is to find the total weight of the edges between every pair of vertices in graph floyd' algorithm can be used to solve this problem some graph algorithms take exponential time and are therefore not practical for graphs with more than few vertices questions these questions are intended as self-test for readers answers may be found in appendix the weight in weighted graph is property of the graph' in weighted graphthe minimum spanning tree (msttries to minimize the number of edges from the starting vertex to specified vertex the number of edges connecting all the vertices the total weight of the edges from the starting vertex to specified vertex the total weight of edges connecting all the vertices