function will be unbounded howeverin some taskswe are able to assign finite capacity to each uncapacitated edge escaping such situation notes minimum spanning tree minimum spanning tree or minimum weight spanning tree is then spanning tree with weight less than or equal to the weight of every other spanning tree more generallyany undirected graph (not necessarily connectedhas minimum spanning forestwhich is union of minimum spanning trees for its connected components one example would be cable tv company laying cable to new neighborhood if it is constrained to bury the cable only along certain pathsthen there would be graph representing which points are connected by those paths some of those paths might be more expensivebecause they are longeror require the cable to be buried deeperthese paths would be represented by edges with larger weights spanning tree for that graph would be subset of those paths that has no cycles but still connects to every house there might be several spanning trees possible minimum spanning tree would be one with the lowest total cost figure minimum spanning tree graph minimum spanning tree tree for (total cost graph may have many spanning treesfor instance the complete graph on four vertices has sixteen spanning treesfigure complete graph with four vertices lovely professional university