Abstract Temporal networks capture systems whose interactions occur as time-stamped events, where resilience depends on whether time-respecting connectivity can be maintained under disruptions. Existing assessments often rely on static aggregation or path-centric indicators, which may overlook higher-order redundancy that emerges and dissolves over time. We propose a persistence-aware, cycle-driven framework that treats recurrent temporal cycles as resilience-relevant building blocks. The method detects cycles within sliding windows, tracks their recurrence to quantify persistence, and encodes cycles that exceed a persistence threshold as hyperedges in a temporal hypernetwork. Based on this representation, we introduce two dynamic node-level metrics—Temporal Cycle Number (TCN) and Temporal Cycle Ratio (TCR)—to quantify persistent cycle participation and to identify nodes that anchor durable closure. We evaluate the framework on six real-world temporal networks spanning social, transportation, biological, communication, infrastructure, and economic domains using controlled node-removal experiments and temporal-efficiency loss as the primary impact measure. Under the adopted windowing scheme, datasets, and disruption protocols, TCN and TCR exhibit higher rank-based association with disruption impact than the representative static and temporal baselines considered. Moreover, in the same experimental setting, targeted removal of high-TCN/TCR nodes tends to yield larger efficiency degradation than degree-based attacks, which is consistent with the interpretation that recurrent cycle closure can coincide with time-respecting detours that support connectivity. A direct comparison with persistence-weighted scores derived from non-closed temporal motifs (2-paths) further shows that topological closure, rather than motif persistence alone, is the primary driver of the observed predictive advantage. These findings provide empirical support—within the scope of our evaluation—that persistence is an informative factor when using cycle closure as a redundancy signal, and that hypernetwork-encoded persistent cycles offer a compact and interpretable representation for temporal resilience analysis.
Li et al. (Sun,) studied this question.