Consider the graph and the flow vector of Fig. 1.16.
(a) Enumerate the simple paths and the simple forward paths that start at node 1.
(b) Enumerate the simple cycles and the simple forward cycles of the graph.
(c) Is the graph connected? Is it strongly connected?
(d) Calculate the divergences of all the nodes and verify that they add to 0.
(e) Give an example of a simple path flow that starts at node 1, ends at node 5, involves four arcs, and conforms to the given flow vector.
(f) Suppose that all arcs have arc flow bounds -1 and 5. Enumerate all the simple paths that start at node 1, end at node 5, and are unblocked with
