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5. (21 points) Answer the following questions about the accompanying graph. (a) (3 points) Is the graph complete? If not, give an example illustrating why. Solution: (b) (3 points) Is the graph bipartite? If not, give an edge whose removal would make the graph bipartite. Solution: (c) (3 points) How many paths can you find from node E to C? Give any path(s) you find. Assume for this question that a path is defined as a sequence of distinct nodes from the source to target node. (d) (3 points) Can you find an edge whose removal would disconnect the graph? If so, give one such edge. (e) (3 points) Which 2 nodes have the longest shortest path between them, and what is the path length? Solution: (f) (3 points) What is the average degree of this graph? Average degree is defined as the sum of all nodes' degrees divided by the number of nodes in the graph. Simplify your final answer (report as a reduced fraction or decimal). Solution: (g) (3 points) Now assume this graph is instead directed, where each existing edge is now a directed edge that goes from the node earlier in the alphabet to the node later in the alphabet. Which nodes have in-degree higher than its out-degree? Solution