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Topological states are useful because they are robust against disorder andimperfection. In this study, we consider the effect of disorder and thebreaking of parity symmetry on a topological network system in which the edgestates are protected by Chern numbers. In the absence of periodicity, the localChern number is adopted to characterize the topological features of thenetwork. Our numerical results show that the local Chern number and the edgestates are very robust against onsite disorder as long as the gap of the bulkstate continuum remains open and survives even when the bulk band gap isclosed. Breaking the parity symmetry can destroy the quantization of localChern numbers, compromising the existence of edge modes. We observednon-integer local Chern number peaks that are non-zero inside the bulk bandsbut these non-zero non-integral local Chern numbers are not associated with theexistence of robust edge states.

Disordered transmission-line networks with and without parity symmetry