Error and attack tolerance
Figure 4. The robustness of a complex system against errors and failures can be tested by investigating the effect of removing nodes. (a) Removing the circled nodes causes the network to break into several smaller clusters. (b) The largest cluster decreases in size from 22 nodes to seven when we disconnect three, i.e. 14%, of the nodes. (c) Percolation theory predicts that a random network will break into tiny clusters when a critical fraction, fc, of nodes is removed. This prediction does not hold for scale-free
networks as can be shown by plotting the of size of the largest cluster versus the fraction of nodes removed. Calculations show that the cluster size only falls to zero when all the nodes have been disconnected (green). However, if the most-connected nodes are removed then the scale-free network will break at a small fc. (d) By randomly removing domains from the Internet, we found that more than 80% of the nodes have to fail before the network fragments (green). However, if hackers targeted the most connected nodes (red), then they could achieve the same effect by removing a small fraction of the nodes.