[C-x_C-f]

What do you mean by well-connected topology? If you mean that you can reach every neuron from any neuron then the number of connections you need is asymptotically n log n / 2 (not up to a constant factor or anything, just n log n / 2 on the nose, it's a sharp threshold), see [0]. In general when percolation is done on just n nodes without extra structure, it's called the Erdős–Rényi model [0], and most mathematicians even just call this "the" random graph model.

[0] https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_....

[bob1029]

I think we are on the same page.

https://en.wikipedia.org/wiki/Giant_component#Giant_componen...

[C-x_C-f]

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