When half the nodes of a random graph the size of most real-world networks are removed, the network is destroyed. But when the same procedure is carried out against a scale-free model of a similar size, 'the giant connected component resists even after removing more than 80 per cent of the nodes, and the average distance within it {between nodes} is practically the same as at the beginning
In Niall Ferguson's book, "The Square and the Tower: Networks and Power," he discusses the resilience of different types of networks when subjected to node removal. He highlights a stark contrast in behavior between random graphs, which represent most real-world networks, and scale-free models. When half of the nodes in a random graph are removed, the entire network collapses. This emphasizes how fragile these networks are in the face of significant disruptions.
On the other hand, scale-free networks demonstrate remarkable resilience. Ferguson points out that even after the removal of over 80 percent of the nodes in such networks, a giant connected component remains intact. The average distance between nodes remains almost unchanged, illustrating the robustness of scale-free networks. This resilience is crucial for understanding the stability of various systems, from social networks to the internet.
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