  A recently-proposed class of photonic topological insulators is shown to map
onto Chalker-Coddington-type networks, which were originally formulated to
study disordered quantum Hall systems. Such network models are equivalent to
the Floquet states of periodically-driven lattices. We show that they can
exhibit topologically protected edge states even if all bands have zero Chern
number, which is a characteristic property of Floquet bandstructures. These
edge states can be counted by an adiabatic pumping invariant based on the
winding number of the coefficient of reflection from one edge of the network.
