Information Technology Reference
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probability is high that the failing nodes have only a few links and are of no consequence
to the functioning of the web. Moreover, the diameter of the web is only weakly depen-
dent on these low-degree nodes, so their removal, even in large numbers, does not
change the overall structure of the web, including its diameter. Thus, following Albert
et al
.[
4
], we can say that a scale-free web is more robust against random attacks than is
a random web.
However, modern terrorist networks do not attack at random, nor does the malicious
hacker. These people seek out the weakness in their target and attack where they believe
the web is the most vulnerable, because they want their act to have maximum impact. In
a random network this is of no consequence since all the nodes are equivalent. There-
fore, irrespective of whether an attack on a random network is random or carefully
planned, the result is the same. The degradation produced by the attack will be small
and of little consequence. In the case of the scale-free network the result is dramatically
different. The hacker inserting a virus into a high-degree server can efficiently distribute
damage throughout the web using the web's own connectivity structure to bring it to its
knees. The same is true for terrorists, who attack the highest-degree node in the network
and use the connectivity to amplify the effect of the damage. These attacks make use
of the small diameter of scale-free webs; for example, the diameter of the World Wide
Web, with over 800 million nodes, is approximately 19, and social networks with over
six billion people are believed to have a diameter of around six, as pointed out by Albert
et al
.[
4
]. It is the small diameter of scale-free webs that produces the extreme fragility
with respect to attack on a hub. This small-world property is a consequence of the slow
increase in the average diameter of the web with the number of nodes; it is essentially
logarithmic,
=
ln
N
.
Of course, understanding the robustness of a web can be used to counter-attack terror-
ist webs and to strategically defend one's own web. Gallos
et al
.[
18
] study the tolerance
of scale-free networks under systematic variation of the attack strategy, irrespective of
whether the attack is deliberate or unintentional. Since the web is scale-free the proba-
bility of a node being damaged through failure, error or external attack depends on the
degree
k
of the node. It is not clear how to characterize the probability of damaging a
node because the characteristics of different webs can be distinct. They explain that in
computer networks the hubs usually serve many computers and are built more robustly
than other computers in the web, and consequently their probability of failure is less
than that of the other computers for a given attack. However, one can also argue from
the other point of view and conclude that the nodes with more links are less robust. The
highly connected nodes on a computer web have more traffic and this may make them
more susceptible to failure.
As mentioned above, the intentional attack may be quite efficient by virtue of dis-
rupting the highest-degree nodes first. This implies, of course, that the ordering of the
node connectivity is apparent, as it is for many social networks. However, in terrorist
and other criminal organizations the individual higher in the hierarchy may have more
connections, but they may also be less well known. Thus, the probability of removing
them in an attack is significantly lower than that of removing individuals lower in the
food chain, that is, those with fewer links. In order to proceed beyond this point it is
L
