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- W3128477922 abstract "We investigate the spectrum of the non-backtracking matrix of a graph. In particular, we show how to obtain eigenvectors of the non-backtracking matrix in terms of eigenvectors of a smaller matrix. In doing so, we create a block diagonal decomposition of the non-backtracking matrix, more clearly expressing its eigenvalues. Furthermore, we find an expression for the eigenvalues of the non-backtracking matrix in terms of eigenvalues of the adjacency matrix, and use this to upper-bound the spectral radius of the non-backtracking matrix, and to give a lower bound on the spectrum. Specifically, an upper-bound on the spectral radius is found in terms of the number of nodes and edges of the graph. We also investigate properties of a graph that can be determined by the spectrum. Specifically, we prove that the number of components, the number of degree 1 vertices, and whether or not the graph is bipartite are all determined by the spectrum of the non-backtracking matrix." @default.
- W3128477922 created "2021-02-15" @default.
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- W3128477922 date "2021-06-01" @default.
- W3128477922 modified "2023-10-18" @default.
- W3128477922 title "Some spectral properties of the non-backtracking matrix of a graph" @default.
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- W3128477922 doi "https://doi.org/10.1016/j.laa.2021.01.022" @default.
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