Correction to: Nature Physics https://doi.org/10.1038/s41567-020-0924-7, published online 15 June 2020.

In the version of this Article originally published online, in the section ‘Efficient communication is driven by hierarchically modular structure’ the equation for entropy in the second sentence was incorrectly given as \(S = \mathop {\sum }\nolimits_i k_i\log k_i\) and should have been \(S = \frac{1}{{2E}}\mathop {\sum }\nolimits_i k_i\log k_i\). All versions of the Article have been amended.