Consider a directed, edge-weighted graph G with n vertices and its corresponding adja- cency matrix M , where M (i, j) = 0, if i = j w((i, j)), if (i, j) is an edge in G , otherwise Let M 2(i, j) be defined as M 2(i, j) = min{M (i, 1) M (1, j), M (i, 2) M (2, j), ..., M (i, n) M (n, j)} where is regular addition. What does the value of M 2(i, j) tell us about vertices i and j? Also, what does the value of M k(i, j) tell us about vertices i and j, for any 1 k n, where M k(i, j) = min{M k1(i, 1) M (1, j), M k1(i, 2) M (2, j), ..., M k1(i, n) M (n, j)} Hint: Draw some example directed weighted graphs to figure out what the values represent first