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Graph-Theoretic Detection of Anomalies in Supply Chains: A PoR-Based Approach Using Laplacian Flow and Sheaf Theory

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  • Hsiao-Chun Han

    (Department of Computer Science and Engineering, National Chung Hsing University, Taichung City 402202, Taiwan)

  • Der-Chen Huang

    (Department of Computer Science and Engineering, National Chung Hsing University, Taichung City 402202, Taiwan)

Abstract

Based on Graph Balancing Theory, this study proposes an anomaly detection algorithm, the Supply Chain Proof of Relation (PoR), applied to enterprise procurement networks formalized as weighted directed graphs. A mathematical framework is constructed by integrating Laplacian flow conservation and the Sheaf topological coherence principle to identify anomalous nodes whose local characteristics deviate significantly from the global features of the supply network. PoR was empirically implemented on a dataset comprising 856 Taiwanese enterprises, successfully detecting 56 entities exhibiting abnormal behavior. Anomaly intensity was visualized through trend plots, revealing nodes with rapidly increasing deviations. To validate the effectiveness of this detection, the study further analyzed the correlation between internal and external performance metrics. The results demonstrate that anomalous nodes exhibit near-zero correlations, in contrast to the significant correlations observed in normal nodes—indicating a disruption of information consistency. This research establishes a graph-theoretic framework for anomaly detection, presents a mathematical model independent of training data, and highlights the linkage between structural deviations and informational distortions. By incorporating Sheaf Theory, the study enhances the analytical depth of topological consistency. Moreover, this work demonstrates the observability of flow conservation violations within a highly complex, non-physical system such as the supply chain. It completes a logical integration of Sheaf Coherence, Graph Balancing, and High-Dimensional Anomaly Projection, and achieves a cross-mapping between Graph Structural Deviations and Statistical Inconsistencies in weighted directed graphs. This contribution advances the field of graph topology-based statistical anomaly detection, opening new avenues for the methodological integration between physical systems and economic networks.

Suggested Citation

  • Hsiao-Chun Han & Der-Chen Huang, 2025. "Graph-Theoretic Detection of Anomalies in Supply Chains: A PoR-Based Approach Using Laplacian Flow and Sheaf Theory," Mathematics, MDPI, vol. 13(11), pages 1-23, May.
  • Handle: RePEc:gam:jmathe:v:13:y:2025:i:11:p:1795-:d:1666152
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    References listed on IDEAS

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    1. Shiller, Robert J, 1981. "Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?," American Economic Review, American Economic Association, vol. 71(3), pages 421-436, June.
    2. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
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