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Let $G$ be a directed (unweighted) graph with $n$ nodes. We can represent $G$ with an $n \times n$ binary matrix $A$, with $A_{ij} = 1$ if there is an edge $i \to j$ and $A_{ij} = 0$ otherwise.

Assuming $A$ is nonsingular, does $A^{-1}$ have any nice interpretation in the world of graphs?

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