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I think we are on the same page. https://en.wikipedia.org/wiki/Giant_component#Giant_component_in_Erdős–Rényi_model https://en.wikipedia.org/wiki/Giant_compone

• C-x_C-f 2y ago
  Ah but that's a bit different. The giant component doesn't connect all the neurons, only a fraction. The wiki page doesn't say this but if you have c * n / 2 edges then the fraction of neurons in the giant component is 1 + W(-c * exp(-c))/c where W is the Lambert W function [0], also called the product logarithm. As c tends to infinity this fraction tends to 1 but it's never 1. [0] https://en.wikipedia.org/wiki/Lambert_W_function https://en.wikipedia.org/wiki/Lambert_W_function