The topological classification of a system depends on the discrete symmetries of its Hamiltonian. In Floquet photonic waveguide arrays, the abstract symmetries of the Altland-Zirnbauer (AZ) scheme—chiral, particle-hole, and time-reversal (for photonics, $z$-reversal)—arise from structural properties of the lattice, yet a systematic correspondence has not been established. Here, we illustrate this correspondence for a simpler system of one-dimensional waveguide arrays with real coupling coefficients, showing how bipartite structure and $z$-reflection symmetry alone determine the whole AZ class. We further demonstrate that nonbipartite networks—lacking conventional particle-hole symmetry, chiral symmetry, and $z$-reversal symmetry—can nonetheless support topologically protected boundary states at quasienergy $\varepsilon =\pi$, even in one dimension. The protecting symmetry—shifted-particle-hole symmetry—applies equally to higher-dimensional Floquet waveguides.

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• Photonic crystal waveguide
• Symmetry protected topological states
• Topological materials