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RAPH ALGORITHMS determines the 2. Alter the algorithm in this section so that it efficiently ad of yus est path from the start node to every node in the the one destination. that an edge is checked for nodes added to the frin the fringe nodes, or to pick the node to move from th mum spanning tree. 3. Do an analysis of the shortest-path algorithm, counting e, for updating edgs 4. Prove that a breadth-first traversal produces a shortest-path tree for without weights. order in which 5. Prove whether it is always, never, or sometimes true that the order the nodes are added to the shortest-path tree is the same as the which they are encountered in a breadth-first traversal. 6. Prove whether it is always, never, or sometimes true that the order in the nodes are added to the shortest-path tree is the same as th which they are encountered in a depth-first traversal. e orile BICONNECTED COMPONENT ALGORITHM A biconnected component of a graph is the set of three or more nodes fir which there are at least two paths between each node. A biconnected compo- nent can also have just two nodes and one edge connecting them. A bico- nected component is a robust part of a graph because if one node and i are removed from the graph, all of the other nodes in the biconnected comp nent can still reach any other. The graph in Fig. 8.9 shows a connecte that has three biconnected components. The first biconnected compon the nodes labeled A, B, C, and D, the second has the nodes labeled D ts edge and H, and the third has the nodes H and I. Determining the biconnected components of a ne