Topological Uncertainty and Higher-Order Interactions in Spatial Networks
Abstract
Environmental systems are characterized by complex spatial interactions that cannot be fully described through pairwise relationships or local uncertainty measures. We propose a unified framework combining higher-order information theory and topological data analysis to characterize the organization and uncertainty of environmental networks. Spatial entities, represented by monitoring stations or municipalities, are embedded into a Delaunay simplicial complex, and O-information is used to quantify redundancy and synergy among neighboring triplets. The resulting field of higher-order interactions is analyzed through persistent homology, enabling the identification of topological structures that remain stable across interaction scales. The methodology is applied to both an air-quality monitoring network based on weekly NO2 and O3 observations and a multi-hazard territorial assessment. We show that regions exhibiting strong O-information and persistent topological structures correspond to robust environmental patterns, whereas areas characterized by heterogeneous regimes and rapidly varying interactions display increased uncertainty. Building on these results, we introduce a topological uncertainty framework that integrates simplex divergence, higher-order interactions, and topological uncertainty. Our results demonstrate that uncertainty can be interpreted not only as statistical variability but also as the instability of the underlying information topology. By integrating O-information and persistent homology within a common spatial framework, the proposed approach provides a new methodology for detecting robust higher-order structures and topologically uncertain regions in environmental and multi-hazard systems.
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BibTeX
@misc{pomarico2026topological,
title = {{Topological Uncertainty and Higher-Order Interactions in Spatial Networks}},
author = {Domenico Pomarico and Alessandro Fania and Gabriel Ramirez Sanchez and Loredana Bellantuono and Domenico Capolongo and Roberto Cilli and Alessandra Costantino and Davide D' Alo and Mario Elia and Francesco Giordano and Niloofar Kheirkhahan and Raffaele Lafortezza and Raffaele Nutricato and Ester Pantaleo and Sabina Tangaro and Roberto Bellotti and Sebastiano Stramaglia and Alfonso Monaco and Nicola Amoroso},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18439},
eprint = {2609.18439},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18439},
}
RIS
TY - UNPB
TI - Topological Uncertainty and Higher-Order Interactions in Spatial Networks
AU - Domenico Pomarico
AU - Alessandro Fania
AU - Gabriel Ramirez Sanchez
AU - Loredana Bellantuono
AU - Domenico Capolongo
AU - Roberto Cilli
AU - Alessandra Costantino
AU - Davide D' Alo
AU - Mario Elia
AU - Francesco Giordano
AU - Niloofar Kheirkhahan
AU - Raffaele Lafortezza
AU - Raffaele Nutricato
AU - Ester Pantaleo
AU - Sabina Tangaro
AU - Roberto Bellotti
AU - Sebastiano Stramaglia
AU - Alfonso Monaco
AU - Nicola Amoroso
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18439
UR - https://arxiv.org/abs/2609.18439
AB - Environmental systems are characterized by complex spatial interactions that cannot be fully described through pairwise relationships or local uncertainty measures. We propose a unified framework combining higher-order information theory and topological data analysis to characterize the organization and uncertainty of environmental networks. Spatial entities, represented by monitoring stations or municipalities, are embedded into a Delaunay simplicial complex, and O-information is used to quantify redundancy and synergy among neighboring triplets. The resulting field of higher-order interactions is analyzed through persistent homology, enabling the identification of topological structures that remain stable across interaction scales. The methodology is applied to both an air-quality monitoring network based on weekly NO_2 and O_3 observations and a multi-hazard territorial assessment. We show that regions exhibiting strong O-information and persistent topological structures correspond to robust environmental patterns, whereas areas characterized by heterogeneous regimes and rapidly varying interactions display increased uncertainty. Building on these results, we introduce a topological uncertainty framework that integrates simplex divergence, higher-order interactions, and topological uncertainty. Our results demonstrate that uncertainty can be interpreted not only as statistical variability but also as the instability of the underlying information topology. By integrating O-information and persistent homology within a common spatial framework, the proposed approach provides a new methodology for detecting robust higher-order structures and topologically uncertain regions in environmental and multi-hazard systems.
ER -