  Diverse higher-order structures, foundational for supporting a network's
"meta-functions", play a vital role in structure, functionality, and the
emergence of complex dynamics. Nevertheless, the problem of dismantling them
has been consistently overlooked. In this paper, we introduce the concept of
dismantling higher-order structures, with the objective of disrupting not only
network connectivity but also eradicating all higher-order structures in each
branch, thereby ensuring thorough functional paralysis. Given the diversity and
unknown specifics of higher-order structures, identifying and targeting them
individually is not practical or even feasible. Fortunately, their close
association with k-cores arises from their internal high connectivity. Thus, we
transform higher-order structure measurement into measurements on k-cores with
corresponding orders. Furthermore, we propose the Belief Propagation-guided
High-order Dismantling (BPDH) algorithm, minimizing dismantling costs while
achieving maximal disruption to connectivity and higher-order structures,
ultimately converting the network into a forest. BPDH exhibits the explosive
vulnerability of network higher-order structures, counterintuitively showcasing
decreasing dismantling costs with increasing structural complexity. Our
findings offer a novel approach for dismantling malignant networks, emphasizing
the substantial challenges inherent in safeguarding against such malicious
attacks.
