  We elucidate a qualitative difference in rheology between fragile and
network-forming strong liquids. In a flow field, the structural configuration
is distorted in accordance with the flow symmetry, whereas the form of the
interaction potential remains unchanged. The role of this mismatch in the
relaxation mechanism under the flow field is crucial for understanding the
shear-thinning mechanism and differs between strong and fragile glass formers.
In fragile glass formers, shear thinning can be attributed to the shear-induced
reduction of the {\it effective density}. In contrast, in strong glass formers,
the shear-induced reduction of the {\it effective activation energy} is a
possible origin of a significant acceleration in relaxation. Our simple
predictions of the crossover shear rate, $\dot\gamma_{\rm c}$, from Newtonian
to non-Newtonian behaviors can be expressed in terms of experimental
observables: in fragile liquids, $\dot\gamma_{\rm c}=(\rho \partial
\tau_\alpha/\partial \rho)^{-1}$, where $\rho$ and $\tau_\alpha$ are the
density and structural relaxation time, respectively, and in strong liquids,
$\dot\gamma_{\rm c}= (\tau_\alpha\Delta E_0 /T)^{-1} $, where $T$ and $\Delta
E_0$ are the temperature and equilibrium activation energy, respectively. These
predictions are consistent with the results of molecular dynamics simulations
for four different glass formers: two fragile and two strong ones. This
different route to the non-Newtonian flow response is related to differences in
the role of density in the relaxation dynamics.
