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)