2020/07/27 by Leo Torres, Torres, Leo · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2007.13611
openalex publication_date 2020/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.