Graph entropy-based node exposure score for risk assessment in information systems

Abstract
This paper introduces the node exposure score (NES), a topology-based metric that quantifies node exposure in an information system by computing random trees, with a focus on risk identification. NES aligns node exposure with the average infection time if an infection—the period required for a replicable state to reach a node through topological diffusion dynamics—started from any other node. A multi-stage benchmark across Gnutella P2P, Erdős–Rényi, and Barabási–Albert graphs analyzes parameter sensitivity, runtime complexity, epidemiological kinetics, and comparative ranking alignment against seven baseline node invariants using Spearman (SC) and Kendall’s tau (KT) correlations in small- to medium-sized graphs. Aggregated benchmarks demonstrate NES’s superior robustness, achieving global mean scores of $0.98 \pm 0.03$ (SC) and $0.92 \pm 0.06$ (KT). Its high runtime cost indicates that the computation benefits from parallel and high-performance computing (HPC) frameworks, particularly in real-time processing dynamic environments where networks constantly change.
Data availability
No datasets were generated or analyzed during the current study.
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Acknowledgements
This work has been partially supported by the European Union’s Horizon Europe framework program under the project ATLANTIS with grant agreement No.101073909
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S.L. contributed to conceptualization, methodology, software, validation, formal analysis, investigation, writing—original draft, writing—review and editing, and visualization. I.I. contributed to methodology, writing—review and editing, supervision, and project administration. U.R. contributed to supervision and writing—review and editing. F.A. contributed to supervision and writing—review and editing. F.J. contributed to writing—review and editing.
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Segurola-Gil, L., Irigoien, I., Orduna-Urrutia, R. et al. Graph entropy-based node exposure score for risk assessment in information systems. J Supercomput 82, 662 (2026). https://doi.org/10.1007/s11227-026-08806-w
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DOI: https://doi.org/10.1007/s11227-026-08806-w

* The Node Exposure Score (NES) is a topology-based metric for quantifying node exposure in an information system.
* NES aligns node exposure with the average infection time, defined as the period required for a replicable state to reach a node through topological diffusion dynamics starting from any other node.
* A multi-stage benchmark was conducted across Gnutella P2P, Erdős–Rényi, and Barabási–Albert graphs.
* The analysis assessed parameter sensitivity, runtime complexity, epidemiological kinetics, and comparative ranking against seven baseline node invariants using Spearman (SC) and Kendall’s tau (KT) correlations.
* Aggregated benchmarks yielded global mean scores of $0.98 \pm 0.03$ for SC correlation and $0.92 \pm 0.06$ for KT correlation.
* The study was conducted on small- to medium-sized graphs.
* The computation benefits from parallel and high-performance computing (HPC) frameworks for real-time processing in dynamic networks.

The research introduces the Node Exposure Score (NES), a topology-based metric designed to quantify node exposure in information systems, focusing on risk identification. NES correlates node exposure with the average infection time, defined as the time required for a replicable state to reach a node via topological diffusion dynamics starting from any other node. The study benchmarks NES across Gnutella P2P, Erdős–Rényi, and Barabási–Albert graphs, evaluating parameter sensitivity, runtime complexity, and epidemiological kinetics. The evaluation involved comparing NES against seven baseline node invariants using Spearman's correlation (SC) and Kendall’s tau (KT) in small- to medium-sized graphs. Aggregated benchmarks show NES achieves global mean scores of $0.98 \pm 0.03$ for SC and $0.92 \pm 0.06$ for KT when compared against the baselines. The high computational cost of the metric suggests that its utility in dynamic environments depends on leveraging parallel and high-performance computing frameworks.

The framework moves from abstract graph theory concepts—topology, diffusion dynamics, and entropy measures—to a tangible cybersecurity risk assessment tool. The demonstrated high correlation with established invariants suggests that topological structure offers a robust, mathematically grounded method for capturing emergent risks, bridging the gap between theoretical network science and applied security concerns. The implication is that understanding how information or malicious states propagate across a network (epidemiological kinetics) is directly quantifiable as an exposure risk. However, the reliance on computationally expensive metrics necessitates careful consideration regarding deployment in highly dynamic, real-time systems; the utility hinges not just on correlation quality but also on the practicality of HPC optimization. The pattern suggests that complex phenomena like infection spreading and risk quantification are often best captured by embedding them within the inherent mathematical structures of the network itself, which might lead to novel insights when traditional centrality measures prove insufficient for dynamic states. What assumptions about the reversibility or determinism of topological diffusion are being implicitly leveraged in this assessment? How should the computational cost be weighed against the potential gain in predictive accuracy for immediate security responses?

Graph entropy-based node exposure score for risk assessment in information systems

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Graph entropy-based node exposure score for risk assessment in information systems

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Executive Summary

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