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. 2019 Jul 3;9:9594. doi: 10.1038/s41598-019-46111-0

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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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Delineative representation of minimum spanning trees with reference to the network types. (a) shows a path-like configuration, in which two end nodes are the leafs (light green) of the tree. Such model network has low leaf fraction, high diameter and low betweenness centrality. (b) presents a diagram of a well-balanced network containing five nodes and two hubs creating a “rich club”, constituted by two directly connected nodes with increased centrality. Relatively small amount of leaf nodes prevents the hubs from overloading. (c) is an example of a star-like tree, having a central, overloaded hub (red) connected with all nodes. This network is characterized by high leaf fraction, low diameter and high betweenness centrality. In an extreme form of a path-like network segregation processes prevail, because it takes a lot of steps to transfer information from the initial to the last node, while an extreme star-like network is dominated by integration processes because information flow from all nodes reaches one central hub and overload it.