  In a previous work [Dillon and Nakanishi, Eur.Phys.J B 87, 286 (2014)], we
numerically calculated the transmission coefficient of the two-dimensional
quantum percolation problem and mapped out in detail the three regimes of
localization, i.e., exponentially localized, power-law localized, and
delocalized which had been proposed earlier [Islam and Nakanishi, Phys.Rev. E
77, 061109 (2008)]. We now consider a variation on quantum percolation in which
the hopping integral ($w$) associated with bonds that connect to at least one
diluted site is not zero, but rather a fraction of the hopping integral (V=1)
between non-diluted sites. We study the latter model by calculating quantities
such as the transmission coefficient and the inverse participation ratio and
find the original quantum percolation results to be stable for $w>0$ over a
wide range of energy. In particular, except in the immediate neighborhood of
the band center (where increasing $w$ to just $0.02*V$appears to eliminate
localization effects), increasing $w$ only shifts the boundaries between the 3
regimes but does not eliminate them until $w$ reaches 10%-40% of $V$.
