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. 2019 Aug 23;9:12325. doi: 10.1038/s41598-019-48668-2

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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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The estimation of parameter γ. (a1) The probability distribution of the travel length. Black squares: surveyed results. Red circles: numerical results obtained at γ_L. (a2) The variation of the normalized difference of travel length, $Δ ρ$ , with respect to γ. $Δ ρ$ is minimized at $γ_{L} \approx 3.0$ . (b1) The distribution of city visitation volumes, {s_i}. Black squares: surveyed results. Red circles: numerical results obtained at γ_s. (b2) The variation of the normalized difference of city volume, Δs, with respect to γ. Δs is minimized at about $γ_{s} \approx 2.3$ . (c1) The distribution of the tourist flows, {w_ij} obtained from surveys. (c2) The variation of the normalized difference of tourist flows, Δw, with respect to γ. Δw is minimized at $γ_{L} \approx 3.5$ . The parameter γ used in Eq. (1) is defined as the average of the three optimal parameters, $γ = (γ_{L} + γ_{s} + γ_{w}) \approx 2.9$ .