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. 2020 Sep 15;10:15065. doi: 10.1038/s41598-020-72137-w

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© The Author(s) 2020

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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Spatial diffusion over the OSN life-cycle. (A) Top: Number of new users and the cumulative fraction of registered individuals among total population over the OSN life-cycle. Users are categorized by the time of their registration into Rogers’s adopter types: (1) innovators: first 2.5%, (2) early adopters: next 13.5%, (3) early and late majority and laggards. White background maps: coloured dots depict towns; their size represent the number of adopters over the corresponding period. Black background maps: links depict the number of invitations sent between towns over the corresponding periods. (B) Adoption scales super-linearly with town population. The $β$ coefficient of urban scaling denotes very strong concentration of adoption in the Innovator stage and decreases gradually in later stages. Fitted lines explain the variation in Number of Adopters (log) by $R^{2} = 0.63$ (red), $R^{2} = 0.83$ (green), $R^{2} = 0.97$ (blue). (C) The Probability of Invitations to distant locations is relatively high in the Inventors stage but decreased over the product life-cycle while diffusion became more local. Exponent fits explain the variation of Probability of Invitations (log) with $R^{2} = 0.24$ (red line), $R^{2} = 0.85$ (green line), $R^{2} = 0.92$ (blue line).