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The power of a vertex of a dominance-directed graph is the total number of 1-step and 2-step connections from it to other
vertices. Alternatively, the power of a vertex is the sum of the entries of the ith row of the matrix , where M is
the vertex matrix of the directed graph.
EXAMPLE 8 Example 7 Revisited
Let us rank the five baseball teams in Example 7 according to their powers. From the calculations for the row sums in that
example, we have
Hence, the ranking of the teams according to their powers would be
Exercise Set 11.7
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Construct the vertex matrix for each of the directed graphs illustrated in the accompanying figure.
1.
