Table · dataset · 2026
<b>Dataset:</b>Betweenness Centrality Dictates ‘Core-First’ Cascading Failures In a Full-Scale Aircraft Fluid Network
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<p dir="ltr">This document provides a concise summary of the supplementary data files accompanying the manuscript, 'Betweenness Centrality Dictates 'Core-First' Cascading Failures In a Full-Scale Aircraft Fluid Network'.
Description
These datasets are provided to ensure the reproducibility and independent verification of the reported results, in compliance with the journal's data availability policy.</p><p dir="ltr"><b>(1) BP_Refinery_Network_Data.xlsx</b></p><p dir="ltr">This dataset contains the complete, analyzed network topology used for the retrospective validation of the coupled topology-dynamics model against the historical industrial cascade event.
The data, comprising 156 nodes and 284 directed edges, were reconstructed from publicly available Piping and Instrumentation Diagrams (P&IDs) from the U.S. Chemical Safety Board (CSB) investigation report. The workbook includes the calibrated node betweenness centrality values and edge weight parameters, which are essential for independently reproducing the retrospective prediction of the cascade timing shown in the manuscript (Supplementary Figure S4b).</p><p dir="ltr"><b>(2) Figure</b><b>_</b><b>1_Degree_Distribution_Data.xlsx</b></p><p dir="ltr">The exact statistical distribution data for the original aircraft fluid network are provided in this file.
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It contains the empirical and fitted degree distributions, including the histograms, bimodal fit, and complementary cumulative distribution function (CCDF). These data serve as the source for Figure 1 of the main text and also act as benchmark reference targets for the synthetic network generator described in Supplementary Information S6.</p><p dir="ltr"><b>(3) Figure</b><b>_</b><b>3_Source_Data.xlsx</b></p><p dir="ltr">This comprehensive dataset underpins the core finding of the 'core-first' cascade propagation, as presented in Figure 3.
It includes the complete time-resolved health matrix for all 237 nodes, the temporal evolution of the failed-node count and propagation velocity, and the power-law fit for the failure time versus betweenness centrality scaling. The robustness of this scaling is further supported by the distribution of the scaling exponent and coefficient of determination derived from 100 independent simulations.</p><p dir="ltr"><b>(4) Figure</b><b>_</b><b>4_Cascade_Failure_Data_complete.xlsx</b></p><p dir="ltr">All time-series data for the cascade failure comparison before and after the hybrid resilience optimization are compiled in this file.
It provides the Effective Failed Count (EFC) and Failure Fraction for the original network and four distinct mitigation strategies (topology optimization, local reinforcement, intelligent isolation, and the hybrid approach). These data are the source for Figure 4 and Table 2, demonstrating the 31.4% improvement in the dynamic resilience index achieved by the combined strategy.</p><p dir="ltr"><b>(5) Supplementary_Fig</b><b>ure</b><b>_</b><b>S</b><b>2_Data.xlsx</b></p><p dir="ltr">This file contains the source data for Supplementary Figure S2, which characterizes the phase transition behavior of the system.
The data illustrate the transition from localized faults to global cascades, identified by a critical propagation threshold. The power-law scaling of the final failure fraction as a function of the distance from this critical point is also provided.</p><p dir="ltr"><b>(6) Supplementary_Figure_</b><b>S</b><b>3_Data.xlsx</b></p><p dir="ltr">The robustness of the power-law failure scaling is further validated in this dataset.
It includes the distribution of the scaling exponent for both peripheral and hub-node initial faults, the multi-fault scaling behavior for intra- and inter-community failures, and a comprehensive comparison of exponent distributions across three distinct fault scenarios.</p><p dir="ltr"><b>(7) Supplementary_</b> <b>Figure</b><b>_S</b><b>1_Edge_Weight_Distribution_Data.xlsx</b></p><p dir="ltr">This dataset provides the distribution of the calibrated edge weights of the fluid network, which is used to inform the fault propagation strength in the model.
The log-normal distribution and the power-law tail of the edge weights are quantified, and these values are directly used in the health evolution equation and the synthetic network generation.</p><p dir="ltr"><b>(8) Supplementary_</b> <b>Figure</b><b>_S</b><b>4_Data.xlsx</b></p><p dir="ltr">The model validation data are presented in this file. It contains the reconstructed topology of the BP Texas City refinery network (nodes and edges), the empirical and simulated pump failure times used for the retrospective prediction (Figure 5), and the component-level validation data for a pneumatic shutoff valve (type V-44).
The calibration curve for the fault propagation strength as a function of the diameter-to-length ratio is also included.</p><p dir="ltr"><b>(9) Supplementary_Table_</b><b>S</b><b>1.xlsx</b></p><p dir="ltr">A summary of the functional node type classification for the aircraft fluid network is detailed in this table. It lists the number and proportion of active control, passive connection, sensor, and tank/vessel nodes, providing a clear description of the system's compositional breakdown.</p><p dir="ltr"><b>(10) Supplementary_Table_</b><b>S</b><b>2.xlsx</b></p><p dir="ltr">The complete set of calibrated model parameters is provided in this table.
It includes the definitions, values, and sources for all key constants and coefficients used in the coupled topology-dynamics model, such as the intrinsic vulnerability coefficients, stress sensitivity, and neighbor failure exponents, ensuring full reproducibility of the simulations.</p><p dir="ltr"><b>(11) Supplementary_Table_</b><b>S</b><b>3.xlsx</b></p><p dir="ltr">This table lists the 'surviving island' subsystems that remained operational after a full-scale cascade failure simulation.
It identifies the functional communities (e.g., cargo ventilation, galley heater) and details the topological mechanism for their survival, specifically relating to the presence of high-betweenness 'bridge' nodes that act as sacrificial fuses.</p><p dir="ltr"><b>(12) Supplementary_Table_</b><b>S</b><b>4.xlsx</b></p><p dir="ltr">A detailed inventory of the hybrid optimization interventions is provided in this table. It specifies the exact nature of the three mitigation strategies—topology optimization (added pipeline lengths), intelligent isolation (valve placements), and local reinforcement (hub nodes reinforced)—along with their justification and estimated costs.</p><p dir="ltr"><b>(13) Supplementary_Table_</b><b>S</b><b>5.xlsx</b></p><p dir="ltr">The target statistical properties and tolerances for the synthetic network generator are defined in this table.
It lists the key topological metrics, such as the number of nodes, edges, Gini coefficient of betweenness, and the power-law exponent, which a synthetic network must match to be considered statistically equivalent to the original aircraft network.</p><p dir="ltr"><b>(14) Synthetic_Network_Example_Output.xlsx</b></p><p dir="ltr">An example output generated by the synthetic network generator script (provided in Supplementary Information S6) is supplied in this file.
It demonstrates that a synthetic network can successfully reproduce key betweenness-related properties within the specified tolerances, thereby validating the generator's utility for independent numerical experimentation and methodological verification.</p><p dir="ltr"><b>(15) Table_1_Key_Hub_Nodes.xlsx</b></p><p dir="ltr">The source data for Table 1 of the main text is provided in this file. It lists the top five hub nodes by normalized betweenness centrality, their functional types, associated systems, and the corresponding simulated failure times.
This table highlights the extreme topological heterogeneity of the system, where a small fraction of nodes carry a disproportionately large share of the network's centrality.</p><p dir="ltr"><b>(16) Table_2_Resilience_Comparison.xlsx</b></p><p dir="ltr">This dataset contains the source data for Table 2, which presents the quantitative comparison of resilience and cost-effectiveness for the five mitigation strategies. It provides the final failure fraction and dynamic resilience index for each scenario, and demonstrates the superior performance of the hybrid strategy.</p>
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