3 problems

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Diagonalizability conjecture for non-backtracking matrices and the 1-shell
Let $G$ be a graph, let its non-backtracking matrix be the matrix whose entries record directed-edge transitions that do not immediately reverse direction, and let the 1-shell of…
Conjectureopenmatrix-diagonalizability non-backtracking-matrices spectral-graph-theoryarXiv posted 2 days ago
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Non-backtracking eigenvector delocalization threshold for Erdős–Rényi graphs
Non-backtracking eigenvector delocalization conjecture. Non-backtracking eigenvector delocalization holds when
Conjecturesolvedeigenvector-delocalization non-backtracking-matrices random-graphsarXiv posted 2 days ago
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Simple outer-eigenvalue conjecture for non-backtracking matrices
Let $G$ be a graph, let its non-backtracking matrix be the matrix whose entries record directed-edge transitions that do not immediately reverse direction, and let an outer eigenva…
Conjectureopennon-backtracking-matrices random-matrices spectral-graph-theoryarXiv posted 2 days ago

Diagonalizability conjecture for non-backtracking matrices and the 1-shell