  Extensive researches have been dedicated to investigating the performance of
real networks and synthetic networks against random failures or intentional
attack guided by degree (degree attack). Degree is one of straightforward
measures to characterize the vitality of a vertex in maintaining the integrity
of the network but not the only one. Damage, the decrease of the largest
component size that was caused by the removal of a vertex, intuitively is a
more destructive guide for intentional attack on networks since the network
functionality is usually measured by the largest component size. However, it is
surprising to find that little is known about behaviors of real networks or
synthetic networks against intentional attack guided by damage (damage attack),
in which adversaries always choose the vertex with the largest damage to
attack.
  In this article, we dedicate our efforts to understanding damage attack and
behaviors of real networks as well as synthetic networks against this attack.
To this end, existing attacking models, statistical properties of damage in
complex networks are first revisited. Then, we present the empirical analysis
results about behaviors of complex networks against damage attack with the
comparisons to degree attack. It is surprising to find a cross-point for
diverse networks before which damage attack is more destructive than degree
attack. Further investigation shows that the existence of cross-point can be
attributed to the fact that: degree attack tends produce networks with more
heterogenous damage distribution than damage attack. Results in this article
strongly suggest that damage attack is one of most destructive attacks and
deserves our research efforts.Our understandings about damage attack may also
shed light on efficient solutions to protect real networks against damage
attack.
