Random Failure: Beyond Scale$-$Free Networks

Calculate the critical threshold fc for networks with

Power law with exponential cutoff.

Lognormal distribution.

Delta distribution $($all nodes have the same degree$).$

Assume that the networks are uncorrelated and infinite. Refer to Table $4\mathrm{.}2$ for the functional form of the distribution and the corresponding first and second moments. Discuss the consequences of the obtained results for network robustness.

Critical Threshold in Correlated Networks

Generate three networks with $104$ nodes, that are assortative, disassortative and neutral and have a power$-$law degree distribution with degree exponent $=2\mathrm{.}2.$ Use the Xalvi$-$Brunet & Sokolov algorithm described in SECTION $7\mathrm{.}5$ to generate the networks. With the help of a computer, study the robustness of the three networks against random failures, and compare their P$($f$)/$P$(0)$ ratio. Which network is the most robust? Can you explain why?