Comparing operational terrorist networks

Abstract

In this paper we provide a presentation of the most popular metrics and systematically apply them to seven terrorist networks studied in the literature and to three new ISIS-affiliated networks. This study then investigates the correlates between structural network characteristics and severity of the attack carried out by the terrorists. Such approach allows us to analyze these networks from several perspectives and to use them to discuss about the security/efficiency trade-off.

Appendix A: Technical appendix

A.1 Centralization

Centralization refers to the variation in actor centrality within a network (Everton and Cunningham 2013, p.97). Following Freeman (1978) and Everton and Cunningham (2013), in this study we take into consideration the degree centralization:

$$ C_{D} = \frac{{\sum}_{i=1}^{g}[C_{\max}-C_{n_{i}}]}{\max{\sum}_{i=1}^{g}[C_{\max}-C_{n_{i}}]} $$

(1)

where $C_{\max \limits }$ is the largest degree centrality score for all actors and $C_{n_{i}}$ is the degree centrality score for actor n_i, and the denominator is the theoretical maximum possible sum of differences in actor degree centrality. The larger is the score, the more likely it is that a single actor is very central whereas the other actors are not. For details see Everton and Cunningham (2013, p. 97).

A.2 Density

Network density is the number of actual connections within the network compared to the total number of possible ties. In an undirected graph density is expressed as:

$$ {\varDelta} = \frac{2L}{g(g-1)} $$

(2)

where L is the number of lines in the network and g the number of nodes. For details see Wasserman and Faust (1994, p. 101).

A.3 Mean nodal degree

The mean nodal degree is a statistic that reports the average degree of the nodes in a graph. In an undirected graph it is expressed as:

$$ \bar{d} = \frac{2L}{g} $$

(3)

For details see Wasserman and Faust (1994, p. 100).

A.4 Clustering coefficient

The clustering coefficient refers to the density of triplets of nodes in an undirected graph and is defined as:

$$ C = \frac{\text{number of closed triplets}}{\text{number of all triplets (open and closed)}}. $$

(4)

The first attempt to measure the coefficient was made by Luce and Perry (1949), for further details see Opsahl and Panzarasa (2009).

A.5 Average path length

This is defined through the average path length of the network and is:

$$ \ell=\frac{1}{g(g-1)}\sum\limits_{i \neq j }^{g}d(i,j) $$

(5)

where d(i,j) denotes the shortest distance between node i and node j; for details see Wasserman and Faust (1994, p. 107).

A.6 Average efficiency

$$ E = \frac{1}{g(g-1)} \sum\limits_{i \ne j }^{g} \frac{1}{d(i,j)} $$

(6)

For details see Latora and Marchiori (2001).

A.7 Global efficiency

$$ E_{\text{Global}} = \frac{E}{E^{\text{Ideal}}} $$

(7)

where E^Ideal is the “ideal” graph wherein all possible edges are present. For details see Latora and Marchiori (2001).

A.8 Betweenness

$$ \text{Betweenness} = \sum\limits_{j<k}g_{jk}(n_{i})/g_{jk} $$

(8)

where g_jk is the number of shortest paths from node j to node k and g_jk(n_i) is the number of those paths that pass through i. Since the value depends on the size of the network we standardize it dividing by (g − 1)(g − 2)/2. For details see Freeman (1978) and Wasserman and Faust (1994, p. 190).

A.9 Closeness

$$ \text{Closeness} = \left( \sum\limits_{j=1}^{g} d(n_{i}, n_{j})\right)^{-1} $$

(9)

where d(n_i,n_j) denotes the number of lines in geodesic linking actors i and j. For details see Wasserman and Faust (1994, p. 183–184).