Critical initiator fraction <i>p_c</i> vs. mean threshold <i>ϕ</i>₀.

<p>(a) ER graphs and (b) SF networks with <i>γ</i> = 3 with average degree <i>z</i> = 10 and system size <i>N</i> = 10⁴. An initiator size above the <i>p</i>_<i>c</i> line leads to global cascades. The analytic estimates (dotted lines) are based on the tree-like approximation [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0143020#pone.0143020.ref014" target="_blank">14</a>] (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0143020#sec002" target="_blank">Materials and Methods</a>).