differences are statistically significant
(greater than three standard deviations), the average path length of the
four networks (except for the gang network) is just slightly greater than their
random counterparts.
These small-world properties imply that terrorists or criminals are able
to connect with any other member in a
network through only a few mediators.
In addition, the networks are sparse,
with very low link density. These properties have important implications for
the communication efficiency of the
networks. Due to the increased risk of
figure 2: cumulative degree distributions:
(a) GsJ network, (b) meth world, (c) gang
network, and (d) Dark web.
Legend
1
Data
GSJ
Power-Law
P(k)
0.1
(a)
0.01
0.001
1
10
k
100
Meth World
1
P(k)
0.1
(b)
0.01
0.001
1
10
k
100
Gang Network
1
P(k)
0.1
(c)
0.01
0.001
1
10
k
100
Dark Web
1
P(k)
0.1
0.01
(d)
0.001
0
10
k
100
being detected by authorities as more
people are involved in a network,
short path length and link sparseness
help lower the risk of detection and
enhance efficiency of communication. As a result, the global efficiency
of each network is compatible to their
random-network counterparts.
On the other hand, a high clustering coefficient contributes to the local
efficiency of all four dark networks.
Previous studies have shown evidence
of groups and teams in these networks
in which members tend to have denser and stronger relationships with one
another. 9, 12 Communication among
group members becomes more efficient, making a crime or an attack
easier to plan, organize, and execute.
We also calculated the path length
of other nodes to central nodes, finding that members in the three studied criminal and terrorist networks
are extremely close to their leaders.
For example, the terrorists in the GSJ
network are on average only 2. 5 links
away from bin Laden himself, meaning his command is able to reach an
arbitrary member through only two
mediators. Similarly, the average path
length to the leader of Meth World is
only three links. 12 Such a short chain
of command also means communication efficiency.
Special attention should be paid to
the Dark Web. Despite the small size
of its giant component ( 80 nodes),
the average path length is 4. 70 links,
only slightly larger than the 4. 20 links
in the GSJ network, which has almost
nine times more nodes. Since hyperlinks help visitors navigate Web pages
and because terrorist Web sites are of-
ten used for soliciting new members
and donations, the relatively long path
length may be due to the reluctance
of terrorist groups to share resources
with other terrorist groups.
Moreover, the dark networks present scale-free properties with power-law degree distributions in the form
of p(k) k-g. Because degree-distribu-tion curves fluctuate, we display the
cumulative degree distributions, P(k),
in a log-log plot (see Figure 2). P(k) is
defined as the probability that an arbitrary node has at least k links. Figure 2
also outlines the fitted power-law distributions. The last two rows of Table
1 report the exponent value, γ, and the
goodness-of-fit, R2, for each network.
Figure 2 shows that all these networks
are scale-free. The power-law distributions fit especially well at the tails.
Note that the three human networks
display two-regime scaling behavior,
which has also been observed in other
empirical networks (such as those involving scientific collaboration). 2
Two mechanisms have been proposed to account for the emergence
of two-regime power-law degree
distributions during the evolution
of a network. 2 First, new links may
emerge between existing network
members. This emergence implies
that criminals or terrorists who were
not related previously could become
related over time. This assumption
is logical since two unacquainted
members could become acquainted
through a third member who knows
each of them. In the GSJ network,
22.6% of the links were post-joining
ties formed among existing members. Second, an existing link may be
table 3: small-world properties of dark networks. each network includes
the metrics in the elicited network (data) and the metrics in the random graph
counterpart (random). numbers in parentheses are standard deviations.
GsJ
Data
4. 20
meth world Gang network Dark web
Random Data Random Data Random Data Random
3. 23 6. 49 4. 52 9. 56 4. 59 4. 70 3. 15
(0.040) (0.056) (0.034) (0.108)
0.55 0.020 0.60 0.005 0.68 0.002 0.47 0.049
(0.0029) (0.0014) (0.0005) (0.0155)
Average Path
length, l
Average
clustering
coefficient, C
Global 0.28
efficiency, e
0.33
(0.004)
0.18 0.23
(0.003)
0.12 0.23
(0.001)
0.30 0.34
(0.019)