  The duality in the Chalker-Coddington network model is examined. We are able
to write down a duality relation for the edge state transmission coefficient,
but only for a specific symmetric Hall geometry. Looking for broader
implication of the duality, we calculate the transmission coefficient $T$ in
terms of the conductivity $\sigma_{xx}$ and $\sigma_{xy}$ in the diffusive
limit. The edge state scattering problem is reduced to solving the diffusion
equation with two boundary conditions
$(\partial_y-(\sigma_{xy})/(\sigma_{xx})\partial_x)\phi=0$ and
$[\partial_x+(\sigma_{xy}-\sigma_{xy}^{lead})/(\sigma_{xx}) \partial_y]\phi=0$.
We find that the resistances in the geometry considered are not necessarily
measures of the resistivity and $\rho_{xx}=L/W R/T h/e^2$ ($R=1-T$) holds only
when $\rho_{xy}$ is quantized. We conclude that duality alone is not sufficient
to explain the experimental findings of Shahar et al and that Landauer-Buttiker
argument does not render the additional condition, contrary to previous
expectation.
