Persistent cycles and network resilience: a hypernetwork-based framework for temporal graph analysis.

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.