Describe how you can represent a n-vertex directed multigraph using an n x n adjacency matrix....

     

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Describe how you can represent a n-vertex directed multigraph using an n x n adjacency matrix. And present algorithms and analyze their complexities for answering the following questions. (a) Given a vertex i, the in-degree and out-degree of i. (b) (c) (d) Given two vertices i and j, report ifj can be reached from i in the graph. Determine if a given directed multigraph is connected or not (i.e, for any vertices i and j, there exists a directed path from i to j.). Report if the graph has a directed cycle. Describe how you can represent a n-vertex directed multigraph using an n x n adjacency matrix. And present algorithms and analyze their complexities for answering the following questions. (a) Given a vertex i, the in-degree and out-degree of i. (b) (c) (d) Given two vertices i and j, report ifj can be reached from i in the graph. Determine if a given directed multigraph is connected or not (i.e, for any vertices i and j, there exists a directed path from i to j.). Report if the graph has a directed cycle.