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Persistent cycles and network resilience: a hypernetwork-based framework for temporal graph analysis.
Baochen Li1,2, Alfiya Abinova2, Shouwei Li3
1School of Aerospace Engineering, Guilin University of Aerospace Technology, Guilin, China.
Scientific Reports
|March 23, 2026
Summary
This study introduces a new framework for analyzing temporal network resilience by focusing on persistent cycles. The proposed metrics, Temporal Cycle Number (TCN) and Temporal Cycle Ratio (TCR), better predict network disruption impacts than existing methods.
Area of Science:
- Network Science
- Complex Systems Analysis
- Temporal Network Theory
Background:
- Temporal networks model time-stamped interactions, crucial for system resilience.
- Existing resilience metrics often miss dynamic, higher-order redundancies.
- Understanding temporal connectivity under disruption is vital across many domains.
Purpose of the Study:
- To develop a novel framework for assessing temporal network resilience.
- To introduce dynamic node-level metrics based on persistent temporal cycles.
- To evaluate the effectiveness of these metrics against existing methods.
Main Methods:
- A persistence-aware, cycle-driven framework using sliding windows to detect recurrent temporal cycles.
- Encoding persistent cycles as hyperedges in a temporal hypernetwork.
- Introducing Temporal Cycle Number (TCN) and Temporal Cycle Ratio (TCR) metrics.
Main Results:
- TCN and TCR show higher association with disruption impact than static and temporal baselines.
- Targeted removal of high-TCN/TCR nodes causes greater efficiency degradation.
- Topological closure, not just motif persistence, drives the predictive advantage.
Conclusions:
- Persistent temporal cycles are key building blocks for network resilience.
- The proposed hypernetwork framework and metrics offer a robust approach to temporal resilience analysis.
- Findings support the use of cycle closure as a dynamic redundancy signal in temporal networks.
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