Meng, Xiangyi, Zhu, Chenxuguang, Pedreschi, Nicola, Chen, Duxin, Hormann, Erik, Dong, Gaogao, and Lambiotte, Renaud (2026) Unifying network connectivity from geodesics to random walks via the random cluster model. Nature Communications, 17. 8187.

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Abstract

Connectivity is a fundamental concept in network science, characterizing how interactions propagate through indirect pathways. While numerous connectivity metrics exist, such as shortest paths, effective resistance and minimum cut, each highlighting distinct structural features, their relationships remain largely fragmented. Here we show that these classical notions arise as limiting cases of a unified s tatistical-physics f ramework b ased o n t he r andom c luster ( RC) model, which interprets connectivity as a principled synthesis of series and parallel transmission. By tuning its parameters, the RC model not only recovers classical connectivity measures but also extrapolates into unexplored regimes, leading to emergent notions of connectivity which yield practical tools for network learning tasks. In particular, RC connectivity naturally encodes the kinetics of growing paths, enhancing learning performance in dynamical settings such as epidemic spreading and neurodynamics. By linking structural, dynamical, and learning-based perspectives, RC connectivity establishes a general and interpretable foundation for the analysis of networked systems.

Item ID:	94508
Item Type:	Article (Research - C1)
ISSN:	2041-1723
Copyright Information:	© The Author(s) 2026. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Date Deposited:	28 Oct 2026 00:16
FoR Codes:	49 MATHEMATICAL SCIENCES > 4901 Applied mathematics > 490199 Applied mathematics not elsewhere classified @ 50% 51 PHYSICAL SCIENCES > 5199 Other physical sciences > 519901 Complex physical systems @ 50%
SEO Codes:	28 EXPANDING KNOWLEDGE > 2801 Expanding knowledge > 280118 Expanding knowledge in the mathematical sciences @ 100%
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