<p>(a) ER graphs with <i>z</i> = 10 and <i>N</i> = 10<sup>4</sup>; (b) SF networks with <i>z</i> = 10, <i>γ</i> = 3, and <i>N</i> = 10<sup>4</sup>; (c) high-school network with <i>z</i> = 5.96 and <i>N</i> = 921; (d) facebook network with <i>z</i> = 43 and <i>N</i> = 4039. The mean threshold is <i>ϕ</i><sub>0</sub> = 0.50. The simulations are averaged over one thousand repetitions. (a) and (b) also show the analytic estimates (dotted lines) based on the tree-like approximation (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0143020#sec002" target="_blank">Materials and Methods</a>) [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0143020#pone.0143020.ref014" target="_blank">14</a>].</p
<p><b>A:</b> The number of unique complexes in independent simulations as a function of time: each c...
<p>The transition towards arbitrarily large cascade sizes can be estimated theoretically using Eq. (...
<p><i>S</i> is the fraction of vertices in the largest connected component. <i>d</i> is the average ...
<p>The networks are the same as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal....
<p>The mean threshold is <i>ϕ</i><sub>0</sub> = 0.50 while the standard deviation of the threshold i...
<p>(a) ER graphs and (b) SF networks with <i>γ</i> = 3 with average degree <i>z</i> = 10 and system ...
<p>The mean threshold is <i>ϕ</i><sub>0</sub> = 0.50 while the standard deviation of the threshold i...
<p>The average size and frequency of global cascades in simulations are shown by red circles and blu...
<p>Distributions of closed triples corresponding to (a) , (b) , (c) , and (d) loops in the Epinions...
<p>Results for the mean number of closed triples corresponding to (a) , (b) , (c) , and (d) loops f...
<p>Results for the mean number of closed triples corresponding to (a) , (b) , (c) , and (d) loops f...
<p>Results of simulating our model at equilibrium as a function of varying network size and structur...
<p>Results of simulating our model at equilibrium as a function of varying network size and structur...
peer-reviewedWe present an analytical approach to determining the expected cascade size in a broad r...
<p>for various initiator fractions <i>p</i> = 0.05 (blue), <i>p</i> = 0.15 (red) and <i>p</i> = 0.25...
<p><b>A:</b> The number of unique complexes in independent simulations as a function of time: each c...
<p>The transition towards arbitrarily large cascade sizes can be estimated theoretically using Eq. (...
<p><i>S</i> is the fraction of vertices in the largest connected component. <i>d</i> is the average ...
<p>The networks are the same as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal....
<p>The mean threshold is <i>ϕ</i><sub>0</sub> = 0.50 while the standard deviation of the threshold i...
<p>(a) ER graphs and (b) SF networks with <i>γ</i> = 3 with average degree <i>z</i> = 10 and system ...
<p>The mean threshold is <i>ϕ</i><sub>0</sub> = 0.50 while the standard deviation of the threshold i...
<p>The average size and frequency of global cascades in simulations are shown by red circles and blu...
<p>Distributions of closed triples corresponding to (a) , (b) , (c) , and (d) loops in the Epinions...
<p>Results for the mean number of closed triples corresponding to (a) , (b) , (c) , and (d) loops f...
<p>Results for the mean number of closed triples corresponding to (a) , (b) , (c) , and (d) loops f...
<p>Results of simulating our model at equilibrium as a function of varying network size and structur...
<p>Results of simulating our model at equilibrium as a function of varying network size and structur...
peer-reviewedWe present an analytical approach to determining the expected cascade size in a broad r...
<p>for various initiator fractions <i>p</i> = 0.05 (blue), <i>p</i> = 0.15 (red) and <i>p</i> = 0.25...
<p><b>A:</b> The number of unique complexes in independent simulations as a function of time: each c...
<p>The transition towards arbitrarily large cascade sizes can be estimated theoretically using Eq. (...
<p><i>S</i> is the fraction of vertices in the largest connected component. <i>d</i> is the average ...