  A network model that can describe light propagation in one-dimensional
ring-resonator arrays with a dimer structure is studied as a
Su-Schrieffer-Heeger-type Floquet network. The model can be regarded as a
Floquet system without periodic driving and exhibits quasienergy band
structures of the ring propagation phase. Resulting band gaps support
deterministic edge states depending on hopping S-matrices between adjacent
rings. The number of edge states is one if the Zak phase is $\pi$. If the Zak
phase is 0, the number is either zero or two. The criterion of the latter
number is given analytically in terms of the reflection matrix of the
semi-infinite system. These properties are directly verified by changing
S-matrix parameters and boundary condition continuously.
