IV. A graph is a finite set of objects called nodes, together with some paths between some of the nodes, as illustrated below. A path of length one i a path that directly connects one node to another. A path of length # is a path made up of # consecutive paths of length one. The same length one path can appear more than once in a longer path; for example, 1-2-1 6 a path of length two from node 1 to itself in the example below. (15 points) (a) Determine the adjacent matrix that describes the graph below. (5 points ) 2 (b) Calculate AZ. (5 points) () What are the paths of length two from node 2 to itself? (4 points)