  The microstructure and electrical transport of Cr$_x$(SiO$_2$)$_{1-x}$
nanogranular films with Cr volume faction $x$$\simeq$0.67 and 0.72 are
systematically investigated. The transmission electron microscopy images and
elemental mappings indicate that the films are quite inhomogeneous: some Cr
granules directly connect to others while some Cr granules with size $\sim$1 to
$\sim$3\,nm disperse in the SiO$_2$ dielectric matrix. For each film, the Hall
coefficient $R_H$ varies linearly with the natural logarithm of temperature,
i.e., $\Delta R_H$$\propto$$\ln T$, above $\sim$60\,K, saturates at
$\sim$60\,K, and retains the saturating value below $\sim$60\,K. The
temperature dependence of Hall coefficient can be explained by the recent
theory in granular metals and originates from \emph{virtual diffusion} of
electrons through the metallic granules. For the conductivity $\sigma$, a
robust $\Delta \sigma$$\propto$$\sqrt{T}$ law is observed from $\sim$50 down to
2\,K. The behavior of the conductivity stems from the ``Altshuler-Aronov"
correction, whose influence on the Hall coefficient is not present in the
films.
