  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 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 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
