Find the adjacency matrices for the directed graphs in (a) and (b) (in attachment).

Two vertices in a graph are adjacent if there exists an edge between them. The entry in row i and column j of the adjacency matrix for a graph is the number of one-edge paths that take you from vertex i to vertex j.

(a)

• None of the vertices have edges that connect them to themselves

• v₁ shares 2 edges with v₂ and 1 edge with v₃

• v₂ shares 2 edges with v₁ and no edges with v₃

• v₃ shares 1 edge with v₁ and none with v₂

So, the adjacency matrix is

(b)

• Only v₁ has a loop that connects it to itself

• v₁ shares 2 edges with v₃ and none with either of v₂ or v₄

• v₂ shares 1 edge with v₃ and none with either v₁ or v₄

• v₃ shares 2 edges with v₁, 1 with v₂, and 2 with v₄

• v₄ shares 2 edges with v₃ and none with either v₁ or v₂

The adjacency matrix is then