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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.04538 |
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Table of Contents:
- Modern society relies on complex supply chains to sustain the flow of goods and services that are essential to daily life. While traditional supply chain theory assumes a clear, hierarchical flow from upstream suppliers to downstream customers, observable real-world transaction networks rarely exhibit this acyclic structure. Instead, detailed inter-firm data reveal that interwoven networks are heavily entangled by cyclic flows. Consequently, without appropriate partitioning of these massive inter-firm networks, the latent flow-hierarchical structures that are central to supply chain concepts remain obscure. To address this analytical challenge, we introduce the flow-Hierarchical Community Network Extraction (f-HiCoNE) framework. By applying combinatorial Hodge decomposition, this approach disentangles the complex inter-firm network by isolating the acyclic gradient flow to quantify the flow-hierarchical parts and partition the graph. By applying f-HiCoNE to a nationwide transaction dataset of approximately 650,000 firms, we successfully extracted functional supply-chain clusters. These clusters demonstrated strong flow-hierarchical organisation, wherein the upstream-downstream positioning of firms was accurately captured by local scalar potentials, revealing distinct geographically localised industrial ecosystems. This study provides a map that helps firms understand their surrounding environment and locate their position within an inter-firm network and opens a new research avenue focused on flow-hierarchy clustering in supply chain analysis.