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An adjacency matrix is a square (0,1)-matrix used to represent a graph. Its entries indicate whether pairs of vertices are adjacent or not.
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When does a row standardized adjacency matrix have a real spectrum?
If the adjacency matrix is $A,$ the "row-standardized" matrix is $DA$, where $D$ is a diagonal matrix all of whose diagonal entries are positive, so has a positive diagonal square root $D^{1/2}$. Now, …