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The adjacency matrix of a non-oriented connected graph is symmetric, hence its spectrum is real. If the graph is bipartite, then the spectrum of its adjacency matrix is symmetric about 0. A few ...

Let $A$ be an adjacency matrix of undirected graph $G$, where $G$ is a connected graph. The normalized adjacency matrix is defined as $\hat{A}=D^{-1/2}AD^{-1/2}$, where $D$ is degree matrix of graph $...

Let $A$ and $\widetilde A$ be the adjacency matrices of a graph $G$ and of its complement, respectively. Is there any relation between the eigenvalues of $A + \widetilde A$ and the eigenvalues of $A$ ...

If so, could you provide examples and specify the conditions under which this occurs? Thank you in advance

As noted in 1806.05647, given a symmetric matrix $A$, the leading eigenvector value problem (LEVP) $$Av = \lambda v,$$ where $A = A^T \in \mathbb{R}^{n \times n}$, $\lambda$ is the largest ...

A colleague in spatial statistics was looking at a map with about 600 regions. For the application she's considering, the induced adjacency matrix had some undesirable properties (where two regions ...