Figure 1

Relative size of the largest connected component of a random graph, as a function of 2× the average number of fixed-strength connections between vertices. W is the Lambert-W function, or the ProductLog in Mathematica, which solves the relation W(x) exp[W(x)] = x. Note the sharp threshold at a = 1, and the subsequent topping-out.'Tuning' the giant component by changing network topology generally leads to a family of similar curves, those having progressively higher threshold having correspondingly lower asymptotic limits (e.g. [41], fig. 4).