  We report measurements of Little-Parks oscillation on the hierarchical
honeycomb-superconducting network for investigating possible effects of
hierarchical structure in terms of spatial symmetry, parity and duality. We
observed an asymmetric Little-Parks oscillation about $\Phi/\Phi_0 = 1/2$,
although spatial symmetry was kept in the network. In comparison with a regular
honeycomb network, the asymmetric oscillation is attributed to hierarchy which
induces mixture of commensurate and incommensurate regions. The asymmetric
oscillation is found to indicate breaking of the duality of vortex
configuration.
