  We describe the non-backtracking spectrum of a stochastic block model with
connection probabilities $p_{\mathrm{in}}, p_{\mathrm{out}} = \omega(\log
n)/n$. In this regime we answer a question posed in Dall'Amico and al. (2019)
regarding the existence of a real eigenvalue `inside' the bulk, close to the
location $\frac{p_{\mathrm{in}}+ p_{\mathrm{out}}}{p_{\mathrm{in}}-
p_{\mathrm{out}}}$. We also introduce a variant of the Bauer-Fike theorem well
suited for perturbations of quadratic eigenvalue problems, and which could be
of independent interest.
