For the given graph, what does the following matrix represent?
For the given graph, what does the following matrix represent?
Graph: vertices V1, V2, V3, V4 with edges e1 = V1–V3, e2 = V3–V4, e3 = V2–V3, e4 = V2–V4, e5 = V1–V4.
Matrix (rows and columns v1, v2, v3, v4):
[ 0 0 1 1 ]
[ 0 0 1 1 ]
[ 1 1 0 1 ]
[ 1 1 1 0 ]
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Correct answer: (A) Adjacency matrix
Explanation
The matrix is square, vertex by vertex, and entry (i, j) = 1 exactly when vi and vj are joined by an edge. For example, V1 is joined to V3 and V4. So it is the adjacency matrix. An incidence matrix would be vertex by edge.