We present transport measurement results on superconducting Nb films with diluted triangular arrays (honeycomb and kagom{e}) of holes. The patterned films have large disk-shaped interstitial regions even when the edge-to-edge separations between near
est 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 shows that these structures observed in honeycomb and kagom{e} hole arrays resemble those in wire networks with triangular and $T_3$ symmetries, respectively. Our 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 arrays
