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. 2019 Oct 23;10:4817. doi: 10.1038/s41467-019-12809-y

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© The Author(s) 2019

Open Access 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 license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license 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 license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 3 — Comparison between the observed Φ and Φ_h of the heterogeneous random null model. Matrices of flows between hotspots levels for the a empirical mobility network of New York City, and b the randomized one obtained from Eq. (2). c Flow-hierarchy for the randomized network and the corresponding empirical data for a subset of US cities, indicating that real cities are significantly more hierarchical than their randomized versions