Identity and Trust in Covert Networks: A Laboratory Experiment

This is the final in an ongoing series of posts on be I writing on models of identity, persuasion and leadership that is in conjunction with a seminar I am currently taking on the subject. This post represents the culmination of ideas for future research in this area. I welcome all comments and critiques.

Covert organizations operate through sparse network structures, which have evolved naturally to support their security and operational needs. These structures have emerged as a result of the inherently dangerous environment in which these organizations exist. terrorist and criminal groups face a significant asymmetric threat from military, law enforcement, etc., and thus are in constant need of new membership to replenish lost personnel and increase their level of available resources (e.g., financial, intellectual, physical, etc.). Thus, the question remains: How are covert organization able to emerge and successfully operate under severe asymmetric threat? In the following research I present a simple model of interactions among a layered set of actors, first belonging to one of two macro-types; A or B, as well as one of three micro-groups; coverts, enforcers or citizens. The model attempts to examine how members of covert networks cope with this dilemma by using both the perceived identity of actors and their current social network to explore how groups bound by the requirements described above emerge successfully or fail. Using proposed agent-base model and a subsequent laboratory experiment this research seeks to propose how these tools might be used to investigate the relationship between identity and covert organization networks

Introduction

Global criminal and terrorist groups do not organize in traditional top-down hierarchical structures of command and control. Rather, these covert organizations operate through sparse network structures, which have evolved naturally to support their security and operational needs. At the same time, terrorist and criminal groups face a significant asymmetric threat from military, law enforcement, etc., and thus are in constant need of new membership to replenish lost personnel and increase their level of available resources (e.g., financial, intellectual, physical, etc.). Given this asymmetry, and the intense scrutiny that terrorist networks receive, trust is the primary currency used to adjudicate both the formation of new of ties and the expulsion of “bad” ties in these covert networks. As a matter of practice, covert networks face a serious dilemma: under constant siege from outside infiltrators, network members must attempt to grow the network in order to survive, while at the same time minimize their potential exposure to infiltrators.

In the following research I present a simple model of interactions among a layered set of actors, first belonging to one of two macro-types; A or B, as well as one of three micro-groups; coverts, enforcers or citizens. The model attempts to examine how members of covert networks cope with this dilemma by using both the perceived identity of actors and their current social network to explore how groups bound by the requirements described above emerge successfully or fail. This research is inspired by the agent-based framework proposed in Hammond and Axelrod 2006[3] and the network-based laboratory experiments presented by Kearns, et al 2009[7], and draws on substantive and methodological themes from both. The paper proceeds as follows: first, I provide a brief description of the motivation for this research, and review the previous literature in this area. Next, the model of interaction among these groups is presented, and various claims regarding the expectations are made from the game setup. In the final section I describe a potential implementation of the game as a laboratory experiment, and present an discussion of using agent-based modeling techniques to help prototype the game’s deign.

Models of Terrorist Organization

Within the literature on terrorism there exists broadly two schools of thought on how these covert organizations recruit members and organize their operations. For those in the Hoffman school, lead by Bruce Hoffman and derived primarily from his book Inside Terrorism[4]. Their claim is that terrorist organizations are lead by a core set of elites, whom delegate various task (e.g., recruiting, finance, targeting, etc.) to their subordinates, who then further delegate, and so on. While those who claim this type of organizational dynamic also acknowledge the relatively flat structure of terrorist groups, this perspective is one of a top-down and leader-centric model. In contrast, the Sageman school, lead by Marc Sageman and likewise derived primarily from his book Leaderless Jihad: Terror Networks in the Twenty-First Century[13]. In the Sageman model, terrorist groups are formed as a function of their social interactions with others, leading to terror cells simply being a “bunch of guys” with little to no real connection to the global jihadist movement. Contrary to the Hoffman model, Sageman posits that terrorists groups exists as sparsely connected cells throughout the world, acting in most cases as autonomously; only receiving inspiration from the global movement.

This divergence of views was bore out in a series of articles published in Foreign Affairs magazine[5,6], wherein each author attempted to show the error in the other’s model. In reality, however, it is likely that the organizational dynamics terrorist groups is some hybrid of these two perspective, as terrorist must constantly reorganize themselves as a reaction to pressure from international military and law enforcement agencies. Also, while each of these perspectives are valuable conceptual models of terrorist organizations, both are largely derived from each authors’ own intimate knowledge of terrorism (e.g., Marc Sageman worked as a CIA case officer in Beirut for many years) or in-depth case studies with limited breadth.

There has been little formal work into the organization of terrorist groups. Of the work that has been done, the vast majority have attempted to develop models that illustrate the decision calculus of individual terrorist, or treat organizations a single rational entities. Much of the research in this field has focused on the rationality of various terrorist tactics—such as suicide terrorism[9,10]. In this vein, other research has examined how terrorist groups attempt to maximize expected utility when determining what people or places to target[8]. Furthermore, several researchers have isolated specific terrorist situation, and developed models to explain behavior in these circumstances; such as a hostage scenario or nuclear proliferation[12]. In all of these models; however, the structure of the terrorist organizations are assumed as a primitive constant of the model, or ignored completely.

Within the social networks literature there are several theoretical models of human organization. The so-called “small-world” network model was introduced by Watts and Strogatz[15], and was predicated on two important observations in social networks: short average path length between vertices, and a high level of clustering among vertices. These structural phenomena were often observed in relatively small networks, but as technology improved so did our ability to study large complex networks. Following the Watts-Strogatz model was the work of Barabasi and Albert[1], which noted that structure within complex networks exhibited “preferential attachment,” meaning a limited number of vertices drew in disproportionally more edges than the vast majority of others, creating the now well-known observation of power-law or scale-free degree distributions in complex networks[2]. The ERGM class of models retains the structural consistency of these previously developed models; however, ERGM assume a fixed number of vertices, and structure is derived from a stochastic process[11]. While the literature on random graph models, from Erdos-Renyi to ERGM, has provided enormous insight into the general structural dynamics of networks, these models are based on observations of human dynamics taking place in an open and public forms (i.e., the social networks of a fraternity or the connection patterns of the World Wide Web). The organization of covert terrorist organizations; however, occurs while group members are actively attempting to hide from or deceive those observing them. Current models of social networks; therefore, may be poor approximations of these types of structures.

The following research attempts to build upon both of these literatures by supposing that actors in these covert networks are using identity as a means to determine the relative utility of bringing new members into their organization. In the following section I propose a simple model of covert network emergence, from which I later derive a laboratory experiment to test test the dynamics of emergence.

A Model of Covert Network Emergence

As stated, there are two types of players; either A or B, which can be members of one of three different groups: coverts, enforcers or citizens. As a practical matter, I restrict coverts to be of type and enforcers to type ¹, thus there are total of four type-group possibilities for players. The distribution of players in the game will model the asymmetry described above, such that the number of players from each group will follow and type will be distributed . Before play begins all players are endowed with some amount of resource . For covert and citizen players this resource is endowed with a distribution , while for enforcers , where and is common knowledge among all players. The purpose in modeling resource in this way is two-fold: first, this provides enforcers with an asymmetric advantage for attracting new ties (described below), which makes the play of coverts more difficult; second, it also allows coverts to blend in as citizens, making the play of enforcers more difficult.

Before the game begins, players are are placed on an torus, which forms the landscape of play. Enforcers and citizens are distributed randomly on the torus, but coverts are distributed randomly within -steps of some fixed point on the torus. There are two motivations for this spatial restriction. First, this is meant to increase the ex ante probability that coverts will find each other during at the game’s onset, which is meant to model the observed tendency of covert actors to exists with higher density within subspaces of a given geographic region. Second, because coverts existence in the game is dependent on their ability to form ties with other coverts, if they were also distributed randomly the ex ante probability of their being able to find each other would be prohibitively low. Along with an initial spatial distribution, citizen players are also placed in exogenous social networks. For the general model described here these ties are randomly generated; however, this is a poor model for real human networks. As such, in the a later section I discuss using computer simulations to investigate the advantages and disadvantages of various random graph models of social networks for this exogenous structure.

When play begins, coverts and enforcer players must decide whether to form a tie with one of its immediate neighbors. Since type is common knowledge but group membership is not, players can observe their neighbors’ types and the types of those their neighbors are directly connected to, as well as the density of ties among those second order connections.² When investigating their neighbors, players can also observe the amount of resource each player has and the resources available among the players in a neighbor’s ego-networks. Once these ties have been formed the round ends, and coverts and citizens can move a single step in any of the eight possible directions available to them on the torus (i.e, any of the eight that are not currently occupied by another player). Enforcers use the same mechanisms to adjudicate tie formation, but their play differs in two important ways. First, their mobility on the torus is greatly enhanced, resembling that of the queen in chess; in contrast to that of the coverts and citizens, which is akin to the pawn. Second, as their name suggests, enforcers’ role is to expel coverts from the game; therefore, when they suspect that a member of their network is a covert player they must decide whether to “engage” that player and force it to reveal its group membership. This decision; however, is costly, as enforcers’ utility is directly a function of the number of coverts they can correctly identify, but if an enforcer mistakenly engages a non-covert they are removed from the game.

The primary conflict in the game is that coverts seek to form ties with each other coverts, then co-opt citizens to increase their resources; while enforcers seek to form ties with coverts in order to break up and destroy their networks. In each round of the game, coverts lose a constant amount of resources , which can only be replenished by creating ties with other coverts, or converting citizens players. If a covert enters a round with sufficiently low resources, denoted , they “die” and are removed from the game, and all network connections are severed. In order for coverts to grow their networks, they must first find another covert and form a dyad, then begin to close triangles with citizens. When a citizen is connected with two or more coverts it becomes a covert and the resources are shared. This is a key element of the game, as coverts must work to grow their networks in order to survive, but at the same time remain cognizant of invasion from a enforcers. If a covert forms a tie with an enforcer and is forced to reveal its group membership by that enforcer it is removed from the game and all of its network ties are severed. To induce play, covert player utilities are derived by equation 1 below, and enforcer utility from equation 2. In both equation and is a binary variable to indicate whether a player has been removed from the game at time .

For coverts, if they are never forced to reveal their group membership () their utility is a function of the size of their network, the amount of shared resource in that network, and the total number of rounds they survive. From Equation 1, is to total number players in covert ‘s social network, is network member ‘s resource endowment, and is the number of rounds played. If a covert is forced to reveal their group membership (), utility is equal to player ‘s resource endowment at , when they are removed from the game. For enforcers that never mistakenly engage a non-covert to reveal group membership (), utility is simply a function of the total number of coverts correctly identified, , by the total number of rounds played, . On the other hand, if an enforcer is removed from the game, , or never forces a player to reveal group membership, , their utility is zero.³ With the game setup complete, I now proceed to discuss some potential strategies of play and their expectation for success.

Play Strategies and Expectations

To explore how identity and trust effect the success or failure of covert groups in this simple game I propose two different strategies for covert players. First, there is a \emph{resource maximizing covert} that attempts to form ties with only those nearest neighbors that present the highest expected benefit based on their known level of , and that of their neighbors’. With such a strategy a covert would calculate the expected payoff from forming a tie with one of its neighbors based on the potential wealth the neighbor and its network neighbors could provide. The second strategy is a \emph{trust maximizing covert}, wherein a player decides to form a tie on the perceived ability to trust a neighbor rather than their resources. There are many possible ways to calculate trust, but one simple way would be to only form ties with neighbors whose ego-networks meet some threshold of type membership. In this game; therefore, trust maximizers would would only form ties with neighbors that also achieved some threshold meeting number of second order ties to type A’s.⁴ The assumption driving this strategy is that identity plays a major role in trust, which has been observed across disciplines in the identity literature.

Before designing a laboratory experiment it will be useful to have some expectation of how play will proceed. Using the two basic strategies discussed above it may be possible to form a priori expectation of the success for each strategy, and thus the expected utility maximizing strategy. As a covert’s success is the result of not only their actions but also the decision of an enforcer to engage them I use the variable to represent the presence of an enforcer in a covert’s social network (e.g., if an enforcer is present). The presence of an enforcer in a covert’s network does not necessarily imply that a covert has failed; but rather, if a covert is present than the enforcer must also force the covert to reveal its group membership. For the purposes of this abstraction assume that the probability an enforcer will engage any member of its social network as the random variable such that .

I begin by calculating the probability that an enforcer playing the resource maximizing strategy has an enforcer in their social network; or more precisely, the probability that an enforcer will have the highest level of resource among a resource maximizing covert’s nearest neighbors at time . Assuming equal probability that an enforcer will be at some position on the game torus at any time, this probability is defined in equation 3 below.

From equation 3, the probability is the product of the ratio of enforcers in the game to the total number of players, and the percentile of all enforcers’ resource distribution among all players. With this it is now possible to calculate a resource maximizers expected utility, which is defined in equation 4 below.

To compare strategies, I now calculate expected payoffs for the trust maximizing strategy. The probability in question is the same; however, in this case rather than simply having the highest amount of resource the enforcer must be the most “trustworthy” among all of the covert’s nearest neighbors. Assume that all trust maximizing coverts use a common function to determine trustworthiness, we will define in equation 5 below.

This formula states that for a trust maximizing covert player ‘s trustworthiness is determined first by the density of connections that player has with players of the same type as that covert, in this case the ratio of player ‘s edges with players of type A to all edges. This ratio is then weighted by the difference between player ‘s level of resource and the minimum level of resources given to enforcer agents. That is, negative levels of trust are possible for players whose resource level is relatively higher than . From equation 5, a trust maximizer will thus make a social tie to the player at with the maximum value of among all of that covert’s nearest neighbors. The probability that an enforcer will be in a trust maximizing covert’s social network at time ; therefore, is the probability that an enforcer is the most trustworthy among the nearest neighbors of that covert. By construction; however, for all enforcers, thus this probability will only be a function of the fraction of ties to players of type A an enforcer has.

From equation 6 above, the probability that an enforcer is in a covert’s network at time is the ratio of the sum of all edges enforcer have made with players of type A to the total number of edges present in the game, i.e., the density of enforcer ties to actors of the covert type. The expected utility for coverts playing the trust maximizing strategy is analogous to that of the resource maximizers described in equation 4 above, wherein the probability in equation 6 replaces that of equation 3. This discussion of expected payoffs is meant to highlight two important aspects of play in this game. First, even at this level of abstraction, it is clear that there may be very complex dynamics required to describe how covert actors use identity as a means to growing their social networks. That said, the second point I would like to highlight is that by examining these payoff function and probabilities it appears that ceteris paribus a resource maximizing strategy will out perform a trust maximizer in the long run.

That is, assuming all parameters of decision making are equal (e.g., the values of and are constant for all players), then a player implementing the resource maximizing strategy will on average increase their resource at every time step faster than the trust maximizer. For example, consider two covert players that begin the game with identical resource endowments, but play resource and trust maximizing strategies respectively. Figure 1 below describes their expected payoffs at each time-interval.

If neither player is removed from the game then their long-term expected payoffs diverge quite significantly. For the covert playing trust maximize their long-term expected utility is simply the mean of the or 0.5 due to the construction of resource are distributed among all players. For the resource maximizing player; however, their long-term expected payoff is the mean of the , which in the above example for is 0.8. This finding is a rather extreme abstraction the model proposed above, as it does not account for the vast complexity of decision making that each player must consider even in this relatively simple game; however, it is important to note that when those factors are uniform across players the resource maximizer will always do better because by construction. This is critical, as it indicates using identity information when adjudicating tie formation is not the best strategy given this model proposed above, which contradicts the central hypothesis of this research.

Due to the complexity of the proposed game there are two potentially useful frameworks for fully testing the hypothesis of identity and covert networks. First, a robust computational model, utilizing an agent-based model (ABM) to observe the effectiveness of various strategies for the full gamut of play. From this framework it may be possible to explore how identity and trust act as support mechanism for covert networks and allow them to emerge successfully, even in the face of constant threat from enforcer agents. The limitation to this method is that all results are biased by the assumptions of the designer, i.e., any findings may be the result of elements “programmed in” to the model. Also, and more importantly, the purpose of this research is not to draw conclusions from the path-dependent decisions of a population of computer agents, but rather observe how humans seek to self-organize in the face of persistent threats from their environment.

In that vein, I propose to fully test this research through a laboratory experiment with human players. In the following section I describe the design and implementation of such an experiment. To begin, I discuss the design of a basic ABM to help scope the project size, and create expectations for the number of players of each type. Next, I describe how players would be introduced to the game, and finally I discuss data collection and analysis.

Modeling as a Laboratory Experiment

Central to game proposed in the previous section are the interactions of covert and enforcer players with each other and the citizen players. As such, when attempting to implement this game as a laboratory experiment it will be extremely important to have a low-level understanding of how various initial distribution of player type and group membership affect the outcome of the game. Unfortunately, experimenting with these parameters using human subject is both prohibitively expensive and time consuming; therefore, an alternate method of testing is needed. In this case, I propose using a simple ABM to test how various parameterizations of the game affect the outcome. Specifically, starting with the minimum required set of human agents, a single enforcer and two coverts, then using an ABM to test how different numbers of citizen agents alter the progress of the game.

Along with testing variations in the initial population levels of citizen agents, the ABM will also allow for the testing of how various initial spatial position placement on the torus affects players’ ability to find one another. Recall that covert agents begin play within some -steps from a fixed point on the torus in an effort to increase the a priori probability that they will form a dyad. As such, an examination of the effect of the size of on the ability for computer simulated agents to form ties may inform the ultimate laboratory design. In general, a properly designed and thoroughly exercised ABM implementation of this game will help inform many aspects of game play, even beyond the setup. For example, by fully exercising all of the parameters the ABM may also provide some generally indication for the number of time steps needed for a covert network to grow to a level of relative stasis, or how quickly enforcers can expel coverts.

Finally, because the size and structure of each player’s social networks can determine their success in the game, it will also be useful to examine how various initial network structures affect game dynamics. As previously discussed, there are several random graph models of social networks that may be used to establish players network structure; therefore, in addition to exploring the effect of various game parameter each of these random graph models will also be tested during the ABM prototyping. It should be noted; however, that these findings should only be used as general guides, as it will still be instructive to test various network parameterizations in the laboratory experiment given the critical role networks play in this model.

All of the information generated from these computer simulations will be valuable as I attempt to build the game framework into a laboratory experiment. In the next, and final section, I describe a the game setup and provide examples of materials that both player types would receive. Then, I describe how the game would proceed, and the format of the user-interface. Finally, I discuss the data collection and analysis.

Game Play in the Lab

I propose testing this model in a laboratory setting using a networked computer interface. Implementing the findings from the ABM tests discussed in the previous section to the laboratory version, for every iteration of the game there will be three human players: a single enforcer player, two coverts, and some number of computer simulated citizen players. Before the game begins each player will be presented with an on-screen “game scenario,” which describes the a fictional situation that motivates the game. Within this description each player is informed of their type and group membership and the rule that govern their play. Figures 2 and 3 below present potential examples if these player prompts.

        Welcome to [insert fictional city]

        In [city] there are two tribes [A] and [B], you are an undercover law
        enforcemnt agent from [A].  This morning two criminals from [B] tribe
        escaped a [city] deterntion center. During the escape the two
        detaineesbecame seperated and are currently within [city] attempting
        to reconnect.

        You have been informed that if these criminals are able to reestablish
        contact they have plans to recruit people from [city] in an effort to
        incite a riot.  If they manage to recruit [X] number of citizens with
        [Y] total amount of resources then law enforcement will not be able to
        quell the rioters. Your mission is to prevent this riot by finding
        these criminals and expel them from [city].

        Welcome to [insert fictional city]

        In [city] there are two tribes [A] and [B], you are criminal from
        tribe [A].  This morning you and your partner in crime escaped
        from the [city] detention center, but during the escape you became
        seperated.  You are now alone in the city and  must find your
        partner; luckily, your partner is somewhere within [k] steps
        of your current location.

        If and when you find your partner, your mission is to recruit new
        members to your criminal network in an attempt to incite a riot.
        Citizens from both tribes can be recruited, and you will need
        [X] number of citizens with with [Y] total amount of resources
        in order for [city] law enforcement to be unable to quell the
        riot.  

        BEWARE: An undercover agent from tribe [B] is in [city] and will
        attempt to find you and expel you from the city before you can
        successfully recruit enough citizens.

Once players have digested this information they will be presented with a further on-screen prompt that explains how the game is actually played. Specifically, how each player can move on the grid, how connections are made, the amount of network and player type information they will be provided during each round; and most importantly, how their utilities are calculated and how that translates into monetary payoffs. For coverts they will be further informed as to why they need to replenish their resources, and how they can be removed from the game by enforcers.

When play begins all players are randomly scattered across the play grid, and the human players are then provided a prompt for making ties. The prompt will provide a listing of all the players in the immediate neighborhood, their identity type, and amount of resource. A player can then click on one of its neighbors to examine its ego-network as described above. After examining their neighbors each player adjudicates a social based on their rule set, and the round ends. There will, however, be a time limit to each round so that players cannot deliberate indefinitely about who to make a tie with. This is particular concern to the covert types, because if no ties are made they still lose resource but with no hope of replenishing through growing their network. After the round ends, players then decide where they would like to move on the play grid, and the process is repeated. The game continues until either the enforcers have expelled all coverts from the game, or the number of play rounds reaches some upper-limit.

From here the game proceeds until the coverts have successfully recruited enough citizens to end the game, or the enforcer has found the coverts and forced them to reveal their identity.

Conclusion

There have been many studies that have attempted to understand the decision processes of terrorists or covert organizations. Much of this research has focused on the rational choice of various attack types (e.g., suicide terrorism versus hostage taking), or on optimal targeting decisions. Likewise, there has been considerable research on how people organize in network structures in order to accomplish a given task, though lacking with specific respect to terrorism. Not present among both of these literary tracks; however, is research on how exogenous network structures and the types of people in them affect the how covert organization are able to sustain growth and survive in the presence of constant threat from law enforcement.

The research presented here attempts to investigate this question by designing a simple game wherein players use identity as a means of adjudicating decisions about how to grow their networks, and eventually execute a task. By designing a simple formal model of interactions among players of different types with different group memberships and utility structures I am able to draw limited conclusions about how various play strategies will fair over the long-term. To explore in a deeper and more meaningful way I propose testing this model as a laboratory experiment with human players assuming the roles of the players in the model.

In the final section I describe the game; how each player type would be motivated and how game play would proceed. As this is only a preliminary draft of this research, the intent with this piece was to lay out the formal foundation of the game, and begin to build upon that for the design of a laboratory experiment. It is my hope that from this work a more robust laboratory experiment can be designed, and the roll of identity in covert networks can be fully explored.

¹This assumption models the frequently observed identity divergence between members of terrorist or criminal organizations and those of the military or law enforcement communities. It is also a useful simplification, however, a more complex model could add a second enforcer type with competing interests.

²For a detailed definition of the ego-network see Wasserman and Faust 1994, section 2.3.3[14]

³If all covert players die at some (i.e., cannot create a dyad with another covert before their resources run out), but some enforcers remain in the game at the enforcers receive some fixed value of utility.

⁴A full discussion of way to operationalization of resource maximization and trust maximization are left open, as there are several different possible implementations, and the intent of this piece is to motivate the idea, rather than define all strategy mechanisms.

References

[1] Reka Albert and Albert-Laszlo Barabasi. Statistical mechanics of complex networks. Reviews of Modern Physics, 74(1):47, 2002. Copyright (C) 2009 The American Physical Society

[2] Albert-Laszlo Barabasi and Reka Albert. Emergence of scaling in random networks. cond-mat/9910332, October 1999. Science 286, 509 (1999).

[3] Ross A. Hammond and Robert Axelrod. The Evolution of Ethnocentrism. Journal of Conflict Resolution, 50(6):926{936, 2006.

[4] Bruce Hoffman. Inside Terrorism. Columbia University Press, 0 edition, April 1999.

[5] Bruce Hoffman. The myth of grass-roots terrorism. Foreign Affairs, May/June, 2008.

[6] Bruce Hoffman and Marc Sasgeman. Does osama still call the shots? Foreign Affairs, July/August, 2008.

[7] Michael Kearns, Stephen Judd, Jinsong Tan, and Jennifer Wortman. Behavioral experiments on biased voting in networks. Proceedings of the National Academy of Sciences, 106(5):1347, 1352, 2009.

[8] Peter J. Phillips. Terrorists’ equilibrium choices when no attack method is riskless. SSRN eLibrary, October 2009.

[9] Karen Pittel and Dirk T. G. Rubbelke. Decision processes of a suicide bomber – integrating economics and psychology. SSRN eLibrary, February 2009.

[10] Brian Roberson, Dan Kovenock, and Daniel G. Arce M. Suicide terrorism and the weakest link. SSRN eLibrary, 2009.

[11] Garry Robins, Pip Pattison, Yuval Kalish, and Dean Lusher. An introduction to exponential random graph (p*) models for social networks. Social Networks, 29(2):173{191, May 2007.

[12] Todd Sandler, and Walter Enders. An economic perspective on transnational terrorism. European Journal of Political Economy, 20(2):301{316, June 2004.

[13] Marc Sageman. Leaderless Jihad: Terror Networks in the Twenty-First Century. University of Pennsylvania Press, 2008.

[14] Stanley Wasserman and Katherine Faust. Social network analysis. Cambridge University Press, 1994.

[15] D J Watts and S H Strogatz. Collective dynamics of ‘small-world’ networks. Nature, 393(6684):440, 442, June 1998. PMID: 9623998.

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