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. 2019 Nov 8;9:16283. doi: 10.1038/s41598-019-51539-5

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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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Illustration of the effects in the critical point model. (a) Influence of road network density on critical accumulation. (b) Influence of betweenness centrality (network redundancy) on critical accumulation. (c) Influence of intersection density on critical accumulation. (d) Capacity reduction by bus operations in the network. Panels (a–c) are constructed as follows. We first residualize the x- and y-variables on the other control variables of the critical point model as given in Table 1. Secondly, we add back the unconditional mean of the x- and y-variables to the residuals. Panel (d) is constructed by calculating each network’s capacity at zero bus production and then calculating the relative difference to the observed capacity. The solid black line in each panel corresponds to the linear fit of the scatterplots.