  In this article we consider Wigner matrices $X_N$ with variance profiles
(also called Wigner-type matrices) which are of the form $X_N(i,j) =
\sigma(i/N,j/N) a_{i,j} / \sqrt{N}$ where $\sigma$ is a symmetric real positive
function of $[0,1]^2$ and $\sigma$ will be taken either continuous or piecewise
constant. We prove a large deviation principle for the largest eigenvalue of
those matrices under the same condition of sharp sub-Gaussian bound and for
some other assumptions on $\sigma$. These sub-Gaussian bounds are verified for
example for Gaussian variables, Rademacher variables or uniform variables on
$[- \sqrt{3}, \sqrt{3}]$.
