Consider the undirected graph shown in the following figure. It consists of six nodes A,B,C,D,E,F and ten edges with the shown edge costs 4 1. (5 Points) Run Dijkstra's algorithm to find the shortest paths from node A to all other nodes. 2. (5 Points) Run an algorithm of your choice (e.g., Kruskal, Prim) and find a minimum span- 3. (5 Points) Is the minimum spanning tree of this graph unique? Justify your answer, i.e. (Show the final answer and briefly describe the intermediate steps.) ning tree. (Show the final answer and briefly describe how you got there if the answer is yes, provide a proof; if the answer is no, provide a counter-example and explain why this is the case. 4. (5 Points) Consider the average distance from A to all other nodes, first by following edges on the shortest path tree (a), let's call it dspr; and then following edges on the minimum spanning tree found in (b), let'scalline is greater, dsp or ST? Does the same answer hold for any graph G-(V,E) and node A E V, or is it specific to this example? avg