preferential-attachment links added).
We also randomly removed percentages of links to test the effect of “fake”
links on the results, finding they were
still valid even when we removed 10%
of the links.
Prior research found that network
topology has a significant effect on
a network’s robustness against failure and attacks and that scale-free
networks are robust against failure
(random removal of nodes). 5 Because
we found that the four dark networks
have scale-free properties, we tested
their robustness against only targeted
attacks. We simulated two types of
attacks in the form of node removal:
those targeting hubs and those targeting bridges. While hubs are nodes
that have many links (high degree),
bridges are nodes through which pass
many shortest paths (high “
betweenness”). 10 When simulating the attacks
we distinguished between two attack
strategies: simultaneous removal of a
fraction of the nodes based on a measure (degree or betweenness) without updating the measure after each
removal and progressive removal of
nodes with the measure being updat-
figure 3: Dark-network robustness against attacks: (a) progressive attacks
against the GsJ network and (b) progressive attacks against the Dark web.
two types of attack are hub (filled markers) and bridge (empty markers).
Legend
12
11
10
9
8
S and <s>
7
6
5
4
3
2
1
0
0
S (Hub attacks) <s> (Hub attacks) S (Bridge attacks) <s> (Bridge attacks)
(a)
f
h
f
b
0.2
Fraction of nodes removed
0.4
Legend
4
S (Hub attacks) <s> (Hub attacks) S (Bridge attacks) <s> (Bridge attacks)
3. 5
3
S and <s>
2. 5
2
1. 5
(b)
f
h
1
0.5
0
0
f
b
0.1
0.2 0.3 0.4
Fraction of nodes removed
0.5
ed after each removal.
We plotted the changes in S (the
fraction of the nodes in the giant
component), <s> (the average size of
remaining components), and average path length after some nodes are
removed. We found that progressive
attacks are more devastating than
simultaneous attacks. Progressive
attacks are similar to “cascading failures” in the Internet where an initial
failure might cause a series of failures
because high-traffic volume is redirected to the next bridge node.
Figure 3 (a) and (b) shows the difference between the network reactions to
bridge attacks and to hub attacks. The
critical points, f, at which the network
falls into many small components, are
marked in the figure. The behavior of
Meth World and the gang network is
similar to the behavior of the GSJ network, showing that these terrorist and
criminal networks are more sensitive
to attacks targeting bridges than to
those targeting hubs (fb < fh). However,
in Figure 3(b), fb and fh are very close,
indicating that hub attacks and bridge
attacks are equally effective at disrupting a one-regime scale-free network.
These results are consistent with
findings from a prior study5 that pure
scale-free networks are vulnerable to
both hub and bridge attacks, while
small-world networks are more vulnerable to bridge attacks. In small-world networks consisting of communities and groups, many bridges may
link different communities together.
Intuitively, when they are removed,
the network should quickly fall apart.
Note that a bridge may not necessarily
be a hub since a node connecting two
communities can have as few as two
links. Small-world networks (such as
dark networks) are thus more vulnerable to bridge attacks than to hub attacks.
In the four dark networks we studied, bridges and hubs are usually
not the same nodes. The rank order
correlations between degree and betweenness in GSJ, Meth World, and
the gang network are 0.63, 0.47, and
0.30, respectively. Note that although
bridge attacks are more devastating,
strategies targeting the hubs are also
fairly effective since the networks have
scale-free properties. Hub attacks and
bridge attacks can be equally effec-
