We present results of transport measurements on superconducting Nb films with diluted triangular arrays (honeycomb and kagomé) of holes. The patterned films have large disk-shaped interstitial regions even when the edge-to-edge separations between nearest neighboring holes are comparable to the coherence length. Changes in the field interval of two consecutive minima in the field dependent resistance R(H) curves are observed. In the low field region, fine structures in the R(H) and T(c)(H) curves are identified in both arrays. Comparison of experimental data with calculation results reveals that these structures observed in honeycomb and kagomé hole arrays resemble those in wire networks with triangular and T(3) symmetries, respectively. The findings suggest that even in these specified periodic hole arrays with very large interstitial regions, the low field fine structures are determined by the connectivity of the nanostructures.
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