(a) Consider a greedy algorithm for finding the maximum clique. The greedy algorithm works as follows. 1. Find the node with the maximum degree. Add it to your clique C, that is C = {i}, where i is the node of maximum degree. Remove every node from the network that is not adjacent to it. 2. Among the remaining nodes, and excluding the nodes that are in C already, consider the one with maximum degree in the new network. Again, add it to C and remove every node that is not adjacent to it. 3. Stop when you have a clique. Does that algorithm produce a maximum clique? Why/why not? What is the worst-case run- time complexity of the algorithm?