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Using elementary graph theory, we show the existence of interface chiralmodes in random oriented scattering networks and discuss their topologicalnature. For particular regular networks (e.g. L-lattice, Kagome and triangularnetworks), an explicit mapping with time-periodically driven (Floquet)tight-binding models is found. In that case, the interface chiral modes areidentified as the celebrated anomalous edge states of Floquet topologicalinsulators and their existence is enforced by a symmetry imposed by theassociated network. This work thus generalizes these anomalous chiral statesbeyond Floquet systems, to a class of discrete-time dynamical systems where aperiodic driving in time is not required.

Topological chiral modes in random scattering networks