Practice question · Numerical answer
A three-node network has adjacency matrix with rows (0, 1, 1), (1, 0, 1) and (1, 1, 0). The entry in row 1, column 1 of the square of that matrix counts the walks of length 2 from node 1 back to itself. Compute it.
Hints
- Dot row 1 of the matrix with column 1 of the matrix.
- Row 1 is (0, 1, 1) and column 1 is (0, 1, 1).
Show the answer
2
Why
The entry is 0(0) + 1(1) + 1(1) = 2: you can go out to node 2 and back, or out to node 3 and back. Powers of an adjacency matrix count walks of that length, which turns a graph question into plain matrix multiplication.
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