非回溯谱：酉特征值与可对角化
Non-backtracking Spectrum: Unitary Eigenvalues and Diagonalizability
摘要：
许多研究工作都花在了刻画某些图类的非回溯矩阵的谱上，特别强调首特征值或第二特征向量。很少有人注意到小幅度的特征值，在这里，我们充分刻画了幅度等于1的特征值。我们将这种特征值的多重性与特定子图的存在性联系起来。给出了非回溯矩阵可对角化的充要条件的一个猜想。作为应用，我们建立了Perron特征值的交错型结果。
英文摘要：
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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