  Recently it was shown (I.A.Gruzberg, A. Kl\"umper, W. Nuding and A.
Sedrakyan, Phys.Rev.B 95, 125414 (2017)) that taking into account random
positions of scattering nodes in the network model with $U(1)$ phase disorder
yields a localization length exponent $2.37 \pm 0.011$ for plateau transitions
in the integer quantum Hall effect. This is in striking agreement with the
experimental value of $2.38 \pm 0.06$. Randomness of the network was modeled by
replacing standard scattering nodes of a regular network by pure tunneling
resp.reflection with probability $p$ where the particular value $p=1/3$ was
chosen. Here we investigate the role played by the strength of the geometric
disorder, i.e. the value of $p$. We consider random networks with arbitrary
probability $0 <p<1/2$ for extreme cases and show the presence of a line of
critical points with varying localization length indices having a minimum
located at $p=1/3$.
