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. 2022 Jan 25;12:1322. doi: 10.1038/s41598-022-05439-w

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© The Author(s) 2022

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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Built versus modelled subway network performance is varied. (a) Network to describe Toronto underground subway system. (b–d) Modelled growth to establish mesh to describe subway system. (e–h) Different shortest-walk calculations for the same mesh, generated from d, but with unique proximity coefficient values. (i) Plot relating network cost to travel time for both built (orange) and modelled (black) networks. Trendline is a fourth-order polynomial function. (j) Plot relating network cost to vulnerability for both built (orange) and modelled (black) networks. Trendline is a power function. (k) Plot relating network travel time to vulnerability for both built (orange) and modelled (black) networks. Trendline is an exponential function. All performance values normalized to the largest local value. Modelled performance values displayed on the plots represent performance for the closest modelled point to the built point (orange) along the trendline.