Activity driven model threshold
(A little too long for a comment, and maybe useful)

Assuming that a is supposed to represent the degree of a node, and
using the formulas from Wikipedia for the Pareto distribution, I have 


mean (which I'm assuming is &lt;a&gt;)  =  gamma*epsilon/(gamma-1) 

and
variance (equal to &lt;a^2&gt;-&lt;a&gt;^2, or &lt;a^2&gt;= mean^2  + var) = epsilon^2*gamma/((gamma-1)^2*(gamma-2))


Translating into R code (rather than doing the algebra):

pmean &lt;- function(gamma=2.8,epsilon=0.001) {
    gamma*epsilon/(gamma-1)
}
pvar &lt;- function(gamma=2.8,epsilon=0.001) {
    epsilon^2*gamma/((gamma-1)^2*(gamma-2))
}
prms &lt;- function(gamma=2.8,epsilon=0.001) {
    sqrt(pvar(gamma=gamma,epsilon=epsilon)+ pmean(gamma=gamma,epsilon=epsilon)^2)
}


When I use the value of gamma=2.1 in the figure caption and feed it into equation (4):

2*pmean(gamma=2.1)/(pmean(gamma=2.1)+prms(gamma=2.1))


I get 0.588 (still not right, but closer ... ??)