In a group there are 5 members: m1, m2, m3, m4, m5. A survey wasdistributed to the group with the question: which member of thegroup you value value the most in terms of opinions? The followingwas the result:

Group member Group member of most valued opinion m4 m1 m1 m2 m2 m2 m3 m4 The Survey was in fact designed to figure out who was the most influential person in the group. (a) Draw a directed graph, where the vertices are the member of the group and there is an edge from m; to m is m; was valued the most by member mj. (b) Write the adjacency matrix for such a graph. (c) What edges do you need to add, so that eventually Ak has all entries that are non-zero? (d) Build the matrix D such that Dij represents the smaller number of edges that go from mi to m; (if there is no path from m; to m; then set that entry equal to ). How can you use this matrix to figure out the most influential person in the group?