By Tomer Kalisky, Reuven Cohen, Daniel ben-Avraham, Shlomo Havlin (auth.), Eli Ben-Naim, Hans Frauenfelder, Zoltan Toroczkai (eds.)
This quantity is dedicated to purposes of the strategies of statistical physics to the characterization and modeling of advanced networks. the 1st components of the e-book drawback thought and modeling of networks, whereas the final components survey purposes to a large choice of typical and synthetic networks. the educational studies that include this booklet are meant for college kids and beginners to the sector, and so they represent a contemporary and finished reference for specialists. To this goal, all contributions were rigorously peer-reviewed not just for clinical content material but in addition for self-consistency and clarity.
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7, for larger m the networks are more robust, though they still undergo a transition at a ﬁnite pc . To calculate P∞ (p) one can use the generating function method in conjunc˜ − k)  (to be more exact, p(k) = Θ(K ˜ − k) + Aδ ˜ , tion with p(k) = Θ(K k,K ∞ where A is chosen such that k=0 p(k) = 1 − p). An alternative method is to use the generating functions in conjunction with the new distribution after the attack. 5 4 Fig. 7. Critical probability pc as a function of λ, for networks of size N = 5 · 105 under intentional attack (symbols) .