Attack tolerance

In the context of complex networks, attack tolerance is the network’s robustness meaning the ability to maintain the overall connectivity and diameter of the network as nodes are removed.

If an attack was to be mounted on a network, it would not be through random nodes but ones that were the most significant to the network. Different methods of ranking are utilized to determine the nodes priority in the network.

This form of attack prioritizes the most connected nodes as the most important ones. This takes into account the network changing over time, by analyzing the network as a series of snapshots (j). The equation below calculates the average degree of a node (i) through a time interval [t₁,t_n].

${\displaystyle deg_{G}(i;t_{1},t_{n})=\textstyle {\frac {1}{(N-1)}}\sum _{j=1}^{n}{deg_{G(t_{j})}(i)}}$

This form of attack prioritizes nodes that occur most frequently over a period of time. The equation below calculates the frequency that a node (i) occurs in a time interval [t₁,t_n]. When the node is present during the snapshot then equation is equal to 1, but if the node is not present then it is equal to 0.

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