  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.
