  We study cascading failures in smart grids, where an attacker selectively
compromises the nodes with probabilities proportional to their degrees,
betweenness, or clustering coefficient. This implies that nodes with high
degrees, betweenness, or clustering coefficients are attacked with higher
probability. We mathematically and experimentally analyze the sizes of the
giant components of the networks under different types of targeted attacks, and
compare the results with the corresponding sizes under random attacks. We show
that networks disintegrate faster for targeted attacks compared to random
attacks. A targeted attack on a small fraction of high degree nodes
disintegrates one or both of the networks, whereas both the networks contain
giant components for random attack on the same fraction of nodes. An important
observation is that an attacker has an advantage if it compromises nodes based
on their betweenness, rather than based on degree or clustering coefficient.
  We next study adaptive attacks, where an attacker compromises nodes in
rounds. Here, some nodes are compromised in each round based on their degree,
betweenness or clustering coefficients, instead of compromising all nodes
together. In this case, the degree, betweenness, or clustering coefficient is
calculated before the start of each round, instead of at the beginning. We show
experimentally that an adversary has an advantage in this adaptive approach,
compared to compromising the same number of nodes all at once.

Social and Information Networks;Discrete Mathematics;Machine Learning;Networking and Internet Architecture