Fig. 5. Employing hyper-motifs to analyze the local resilience of the FW network.

Owing to the heterogeneous scales of networks, a direct comparison of the frequency of hyper-motifs across distinct networks is devoid of significance. This stems from the observation that, purely in terms of quantity, networks of a larger scale tend to present an increased count of hyper-motifs. Consequently, we undertake a comparative analysis post-normalization of the hyper-motif occurrences across networks of varying scales, for which the specific methodology is delineated in the “Methods” section. a All kinds of hyper-motifs in $\mathrm{\Pi }\left(\mathrm{2,\; 4}\right)$. b The normalized occurrence frequency of hyper-motifs. c A higher value indicates poorer local resilience, whereas networks characterized by high substitutability tend to demonstrate greater local resilience.