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arXiv · 2007.13611

Non-backtracking Spectrum: Unitary Eigenvalues and Diagonalizability

Leo Torres
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Abstract

Much effort has been spent on characterizing the spectrum of the non-backtracking matrix of certain classes of graphs, with special emphasis on the leading eigenvalue or the second eigenvector. Much less attention has been paid to the eigenvalues of small magnitude; here, we fully characterize the eigenvalues with magnitude equal to one. We relate the multiplicities of such eigenvalues to the existence of specific subgraphs. We formulate a conjecture on necessary and sufficient conditions for the diagonalizability of the non backtracking matrix. As an application, we establish an interlacing-type result for the Perron eigenvalue.

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Leo Torres. 2020-07-27. Non-backtracking Spectrum: Unitary Eigenvalues and Diagonalizability. https://arxiv.org/abs/2007.13611

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