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. 2021 Jul 28;11:15400. doi: 10.1038/s41598-021-94825-x

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© The Author(s) 2021

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 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/.

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Allometric scale. (a) A toy model of 10 nodes. According to the different nodes chosen as roots, it is possible to obtain ten directed versions of the undirected tree (a). (b)–(d) Three directed versions of the tree in (a) with roots equal to, respectively, nodes 5, 7, and 1. Numbers in brackets represent the quantities (A_i, C_i) associated with each node. (e) Maximum spanning tree of the human functional brain network of an individual chosen at random in healthy subjects with directionality induced by choosing node fifty-one as root. Colors in (e) represent anatomical regions according to the grouping of AAL parcellation shown on the right bottom: Dark blue circles: Frontal Lobe; Orange circles: Insula; Light blue circles: Cingulate; Green circles: Temporal Lobe; Red circles: Occipital Lobe; Yellow circles: Parietal Lobe; Grey circles: Deep Grey Matter; Magenta circles: Cerebellum.