论文标题
非折线范围：单一特征值和对角度的性能
Non-backtracking Spectrum: Unitary Eigenvalues and Diagonalizability
论文作者
论文摘要
在表征某些类别类别的非背带矩阵的频谱上，花了很多精力，特别强调了领先的特征值或第二个特征向量。对小规模的特征值的关注要少得多。在这里，我们完全表征了等于一个的特征值。我们将这种特征值的多重性与特定子图的存在联系起来。我们在必要和足够的条件下为非回溯矩阵的对角度差异提出了猜想。作为应用程序，我们为Perron特征值建立了一个相互插型的结果。
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.
