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. 2022 Apr 27;12:6858. doi: 10.1038/s41598-022-10909-2

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© The Author(s) 2022

Open AccessThis 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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Degree distributions of corruption networks are approximated by exponential models with characteristic degrees that seem to approach a constant value with the network growth. Complementary cumulative distributions of the node degree divided by the characteristic degree for each year (indicated by the color code) of the (A) Spanish and (B) Brazilian networks. The insets show the degree distributions for the latest stage of the network of each country. The approximately linear behavior of these curves on a log-linear scale and the good quality collapse of the distributions indicate that the exponential model approximates well the degree distributions. Evolution of the characteristic degree for the (C) Spanish and (D) Brazilian corruption networks. The markers indicate the maximum-likelihood estimate of the characteristic degree in each year and the error bars stand for 95% bootstrap confidence intervals.