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Pairwise similarity of jihadist groups in target and weapon transitions

  • Gian Maria CampedelliEmail author
  • Mihovil Bartulovic
  • Kathleen M. Carley
Research Article

Abstract

Tactical decisions made by jihadist groups can have extremely negative impacts on societies. Studying the characteristics of their attacks over time is therefore crucial to extract relevant knowledge on their operational choices. In light of this, the present study employs transition networks to construct trails and analyze the behavioral patterns of the world’s five most active jihadist groups using open access data on terror attacks from 2001 to 2016. Within this frame, we propose Normalized Transition Similarity (NTS), a coefficient that captures groups’ pairwise similarity in terms of transitions between different temporally ordered sequences of states. For each group, these states respectively map attacked targets, employed weapons, and targets and weapons combined together with respect to the entire sequence of attacks. Analyses show a degree of stability of results among a number of pairs of groups across all trails. With this regard, Al Qaeda and Al Shabaab exhibit the highest NTS scores, while the Taliban and Al Qaeda prove to be the most different groups overall. Finally, potential policy implications and future work directions are also discussed.

Keywords

Transition networks Terrorism Normalized transition similarity Event sequences Security 

Introduction

Terrorism and its multi-fold complex dimensions have been increasingly studied from different perspectives, attracting scholars from several scientific fields. Advanced quantitative techniques, derived from mathematical and statistical sciences have been applied to increase the knowledge on the ways in which this phenomenon evolves and occurs. Although all social phenomena are of interest to the scientific community, terrorism—especially in the last decades—has been capable of fostering unprecedented attention due to the ways in which it has shocked the recent contemporary history. According to [12], from 1970 to 2016, Middle East and North Africa, South Asia and Western Europe were the regions with the highest number of attacks. However, data reveal the global relevance of the issue, considering that in the last four decades terror events have occurred in more than 200 countries in the world. Indeed, the terrorist threat has pushed scientists to provide help through research to counter the phenomenon. Complex systems, statistics, and security studies are few among the several perspectives from which major applied contributions have been made to the study of terrorism. However, pitfalls and stagnation issues have been highlighted by scholars that have hence reported the lack of relevant and informative data as a major problem in terrorism research [41]. This aspect, coupled with the many questions that are still without an answer, calls for continuous improvements both from the institutional side (that should be more willing to collaborate with researchers sharing more detailed and richer data) and from the research side, without stopping the effort to empirically study terrorism, involving a productive multidisciplinary dialogue across countries and fields.

In the attempt to innovate and advance the knowledge on jihadist dynamics from a network science perspective, the present study seeks to explore the behavioral dynamics of the world’s most active jihadist groups to quantify the extent to which these groups show similar or dissimilar tactical choices in their attack sequences. We will propose a pairwise coefficient that maps the similarity of jihadist groups in terms of transitions between targets, weapons and targets and weapons combined. The study will use open access data and will create transition networks and related network trails treating attacks as ordered state sequences. The relevance of investigating the nature of state sequences is strongly related to the inherent nature of terrorism itself. As a matter of fact, the frequent change of tactical and operational decisions by terrorist groups makes it extremely difficult to predict and eventually prevent attacks and consequent damages. While bounded by limited resources and manpower, terrorists usually have at their disposal many different potential scenarios to maximize the utility of their actions. It is thus crucial to improve the knowledge on transitions between different states to understand regularities and irregularities in the behavior of jihadist groups.

This study is an exploration in this direction and opens the path for future research. With regard to results, on one side, the stability of several pairwise similarities across different transition networks testifies how certain groups actually share (or do not share at all) very common behaviors. On the other side, groups that are similar in terms of weapon transitions but very dissimilar in target transitions demonstrate how there is not always a strong connection between the two dimensions, and that the same terrorist goal can be reached by different means, and vice versa.

The rest of the study is organized as follows: the next section presents the background of the study, with a specific focus on related works existing in literature and a brief biographic review of the terrorist groups that are included in the analyses. The “Data” section will thoroughly present the type of information used to perform the analyses, while the fourth section will describe the analytic strategy of the work in detail. It will first introduce the concept of transition networks, then focusing more specifically on the definition and construction of trails for the purposes of the study and will finally develop and present normalized trail similarity. The “Results” section will report and discuss the main outcomes of the study. Finally, the last section will consider the limitation of the work  and outline the several directions for future research.

Background

Related work

The attention of researchers and scientists on terrorism has increased over the last decades. Major global events have fostered the interest of scholars coming from different fields, contributing to enlarge the number of approaches and perspectives applied to the phenomenon [51]. Indeed, these different perspectives have been applied to the study of different dimensions of terrorism. On one hand, part of this heterogeneous community has mainly focused on the actors, and on the way in which groups or individual perpetrators behave and organize themselves to attack and inflict damages to countries, economies and institutions [13, 14, 23]. Many studies within this line of research employed social network analysis as the main framework to map relations between terrorist individuals or groups [26, 38].

On the other hand, scientists have tried to concentrate on proper event dynamics, trying to understand when and how terrorism happens, with the ultimate aim of providing insights to capture its inherent complexity using methods and techniques from a wide realm of disciplines, including physics, mathematics, statistics and economics [8, 32, 37, 46]. Within this stream of research, terrorist target selection has certainly been a long-standing feature of interest for scientific research [10, 50]. Indeed, its importance is related to the fact that building knowledge on this topic can help in designing prevention policies and allocating resources to protect sensible and potential future targets [4]. Targets have been studied and modelled in different ways. [42] have relied on a game-theoretic formal model assuming rational behavior of agents to demonstrate that when intelligence sharing is not linked to deterrence coordination between countries, policies for protecting likely targets are of little help. The diffusion of open access datasets has then progressively facilitated the analysis of terror behavioral patterns. Relying on data-driven models, [43] have developed Bayesian models to detect the dynamics and key points of terrorist target selection processes and [5] employed Bayesian Poisson change point regression models to demonstrate the way in which transnational terrorists adjust their selection of targets in response to target hardening. Their study, conducted for attacks from 1968 to 2007, identified four separate periods and three underlying covariates that can explain this time-clustering process, namely the dominant terrorist influence, countermeasures and state-sponsorship considerations. In [43], the authors compared diversity in target choice among domestic and transnational terrorism. Using a Bayesian reversible jump Markov chain Monte Carlo model, researchers were able to obtain arrival rate changes in both types of terrorism and evaluate the extent to which their target selection was diverse, also from a temporal standpoint. Asal et al. [3] conversely, have applied a zero-inflated negative binomial model to highlight, among the other findings, that there seem to be a calculated logic behind the decision to attack soft targets and to demonstrate how ideology plays a relevant role in this decision, especially when religious motivations are considered. In spite of the growing body of literature around terrorist dynamics and the specific attention over targets, still some questions remain open. First, this is specifically true if we consider that oftentimes, terrorism is treated as a single, unique entity. This working assumption, unfortunately, underestimates the multi-fold nature of terrorist violence, thus failing to control for different motivations, groups and geographic regions. Second, targets are usually analyzed without paying attention to weapons, which constitute a complementary stream of information that can shed more lights on terrorist behavioral aspects. In fact, if understanding which targets are more likely to be hit by a certain group or actor is certainly relevant, it is also important to investigate the type of resources that will be employed to inflict the desired damage.

Groups

Different categories of terrorism exist. Religious terrorism is one of these categories, and within this category stands jihadism. Although other types of terrorism originates from diverted interpretations of religions (e.g., Christian or Jewish terrorism), it is indubitable that jihadism accounts for the large majority of attacks, deaths, damages and consequences in the last decades. Its existence has deeply influenced the recent history and still have a dramatic impact on the security and safety of many countries and people. In this scenario, five terrorist organizations have played a key role, which we have chosen as specific subjects of this analysis, namely the Islamic State, Taliban, Al Qaeda, Boko Haram and Al Shabaab.

The Islamic State (IS) In recent years, the world has experienced the radical and dramatic actions of the IS. While during the 2000s Al Qaeda was the main terrorist actor in the global scenario, since 2007 the IS has slowly started to overcome all the rivals and acquired the role of most critical terrorist threat for many countries in the world. The anomalous nature of this terrorist organization has been emphasized by many. Kurth Cronin [9] stated that the IS cannot be described as a terrorist group, stressing the differences with Al Qaeda. It is indisputable that IS has many features that distinguish it from all the other terrorist groups of the world. Firstly, it has established a caliphate [20]. Secondly, the IS could recruit a number of members, affiliates and fighters, much bigger than any other group. Thirdly, the IS can rely on economic, communication and military resources that no one else possesses in the terrorism scenario [45]. With respect to this, studies show how the IS relies on the power of the Internet to recruit members and to spread its propaganda more than any other group [11, 24, 33].

Taliban Despite [25] simplistically defined its members as “warriors”, the Taliban is an Islamist fundamentalist terrorist group composed of Pashtun tribesmen and Mujahedeen based in Afghanistan. Johnson [21] stresses how the Taliban proved to be a highly adaptive group. Their tactics have evolved over time: the long tradition of conflicts have helped the members of the Taliban to learn and employ different strategies. In spite of a low technological level, their strategies are rather sophisticated. The control of the territory through different methods (e.g.: the institution of shadow governments in rural areas, as noted by Johnson) and the battlefield tactical behaviors demonstrate their skills. In this scenario, the current first aim of the Taliban is to overthrow the Afghan government. For this reason, in the last years the Taliban have mostly targeted police forces [17]. Moreover, it is relevant to note how since the US invasion in 2003, the Taliban have highly increased the use of suicide bombings [21]. With regard to economy revenues, the Taliban rely on opium and heroin smuggling as the first funding source for their activities [39, 47].

Al Qaeda Al Qaeda is the Islamist terrorist organization responsible for the 9/11 attacks. The dawn of Al Qaeda dates to the Soviet invasion in Afghanistan, when its founding leaders Osama bin Laden and Abdullah Azzam were collaborating together in the conflict. Since the tremendous events of 9/11, research on Al Qaeda has increased. After the death of bin Laden in 2013, the organization has reinvented itself to achieve its aims. Nowadays, Al Qaeda is a global organization, decentralized and franchised around a central control group. Currently, Al Qaeda’s main affiliates are Al Shabaab, Al Nusrah Front, Al Qaeda in the Arabian Peninsula (AQAP), Al Qaeda in the Islamic Maghreb, Abdullah Azzam Brigades and Al Qaeda in the Indian Continent [6]. Zehr [52] develops the concept of “Al Qaeda phenomenon” to describe that process that has led to the worldwide proliferation of terrorist organizations similar to Al Qaeda. According to Zehr, Al Qaeda had the power to inspire the IS and many others to join the jihad. A relevant aspect of Al Qaeda is the connection that the organization has with many others groups, relying on the ideology of the Global Jihad. With the rise of the IS, the terrorist narrative has mainly concentrated on these two entities to understand differences, similarities and possible evolutions in the relations between the two. Abu Musab al Zarqawi was helped by Al Qaeda in the foundation of the JTJ, but after his death and with the expansion of the IS, the two organizations started a feud. Indeed, there have been clashes between the IS, Al Qaeda and other groups like Al Nusrah. Holbrook [16] notes that Al Qaeda sought to present the group as a moderate alternative to the IS, but the events of the last years demonstrated that the IS is the leading force in the Jihadist terrorist scenario.

Boko Haram Boko Haram is a Nigerian terrorist group which has first come to the attention of their country chronicles in the early 2000s [36]. Due to its limited geographical range of action, Boko Haram is not directly considered a priority for Western governments and academia. Nevertheless, it poses great challenges to the stability of the area, threatened by its presence. According to many scholars [2, 19, 31, 36], the expansion of Boko Haram in Nigeria has been caused by multiple factors that are independent of the mere religious aspect. These factors are the extreme Nigerian poverty, the weak efforts of the government in countering the terrorist threat and the grievance of large local areas against the institutions. According to these authors, the economic conditions and political opportunities have fueled the Boko Haram expansion. Moreover, [1] includes also the corruption of the government and the failure of the northern elites in implementing Sharia as important causes of the rise of Boko Haram. Despite a first phase in which Boko Haram targeted the Nigerian security forces and mainly utilized“hit and run” strategies, in the last few years the group has started to carry out attacks also against religious and educational institutions and civilians [40]. The strategies have also changed: the group started acting to occupy and conquer territories, increasing the brutality of the attacks [49]. Institute for Economics and Peace [18] also reports how military defeats led to the separation of three factions within Boko Haram in late 2016: a violent one, an Islamic State-aligned and an Al Qaeda-aligned one.

Al ShabaabHarakata al-Shabaab Mujahideen, mostly known as Al Shabaab, is a jihadist terrorist organization which first appeared in the area of Mogadisciu, Somalia, in the early 2000s [15]. In the last years, the group evolved and expanded across different territories. As noted by [35] while the groups covered a marginal role in Somalia in the early stage of its existence, Al Shabaab is now one of the most relevant players in the process of armed opposition against the nascent Somali government (allies included). This transition has also affected the geographic scope of attacks, which has been expanded in the last years, spanning over different adjoining countries. While the political discourse tried to paint the group as in the middle of a gradual receding process, scholars have demonstrated its resistance and resilience, claiming that Al Shabaab benefits from more legitimization compared to the federal government of Somalia [30]. After a longstanding informal relation, since 2012, Al Shabaab has been officially considered part of the Al Qaeda network [22]. The group has presumably killed over 4000 individuals since its birth, in 2006 [18].

Data

The analyses in this work rely on data drawn from the Global Terrorism Database (GTD). The GTD is the most comprehensive and detailed open access dataset on terrorist events at global scale. The GTD originates from data collected by the Pinkerton Global Intelligence Service (PGIS): researchers at PGIS were trained to include information on terrorist events from 1970 to 1997, and in 2006 the START Consortium received funding to continue the data collection and update the dataset [27, 28]. Data collection continues to date, and START releases updated version of the dataset every year. The dataset includes now data on more than 180,000 events. Information has been gathered from different open sources, and events have to meet specific criteria to be included in the database. These criteria are divided into two different levels. The first-level criteria are three and all have to be verified. These mandatory ones are related to the intention and the violence (or immediate threat of violence) of the incident and to the subnational nature of terrorist actors. The second-level criteria are three and the condition is that at least two of them are satisfied. Second-level criteria relate to (1) the specific political, economic, religious or social goal of each act, (2) the evidence of an intention to coerce, intimidate or convey messages to larger audiences than the immediate victims, and (3) the context of action which has to be outside of legitimate warfare activities. Finally, although an event satisfies these two levels and is included in the dataset, an additional filtering mechanism (variable doubter) is introduced to control for conflicting information or acts that may not be of exclusive terrorist nature [44]. As mentioned in the previous section, we have decided to focus on the five most active jihadist groups in terms of plotted attacks from 2001 to 2016 (Fig. 1). Since each event in the GTD may have up to three perpetrators cooperating in a single attack, we calculated the cumulative sum of all the appearances of each group regardless of the fact that the attack was executed by one actor or more. Moreover, we have decided to merge together all the attacks perpetrated by all the factions belonging to the Al Qaeda network that in the dataset were labeled as separate.1 This process identified the Taliban, IS, Boko Haram, Al Shabaab and Al Qaeda as the most active jihadist groups present in the dataset. After group selection, we removed all the attacks for which we cleaned the data, removing all the events that were labeled as of doubtful terrorist nature (relying on the doubter variable). This led to a reduced amount of attacks for each group (Table 1).

Since the temporal dimension is extremely relevant for the aims of our work, we treated events with no precise reported date (at daily unit detail) in two different ways so as not to lose them. If the additional variable approxdate was available, we imputed data relying on the information included. However, if approxdate was not precise enough to derive any type of imputation, we filled missing data using median date based on each month.
Table 1

Number of attacks (original and cleaned) for each of the selected groups

Group

Cleaned N

Attack frequency

First

Last

Taliban

5629

1.04

1/7/01

12/31/16

Islamic State

3562

2.63

4/18/13

12/31/16

Boko Haram

1901

0.70

7/27/09

12/31/16

Al Shabaab

1695

0.47

11/2/07

12/30/16

Al Qaeda

1502

0.26

09/11/01

12/25/16

Fig. 1

Monthly time series of attacks per group (Jan 2001–Dec 2016)

Additionally, we employed data on weapons and targets. In the GTD, each event may have information on multiple weapons and targets: in the analysis we kept all available information, without dropping any variable or specific category, so as not to alter the distribution of events and their specific characteristics. It is worth outlining that the GTD provides different levels of details for both weapon and target features. Weapons are labeled on two different levels of detail. Variable weaptype records the general type of weapons that terrorists used in the attack (e.g., firearms), while variable weapsubtype gives a more detailed and specific type of information related to the weapons used in the event (e.g.: automated weapon). Targets are instead labeled on four different levels of detail. Variable targtype is the most general one, providing a broad class to which the specific target belongs (e.g., government), and targsubtype gives further specification, introducing additional information (e.g., government building/facility/office). Variable corp identifies the corporate entity or government agency that was targeted (e.g.: Spanish government) and variable “target” labels the specific person, building or installation that was victimized. In the present work, we have used in both cases the most general type of categorization (i.e.: variables targtype and weaptype): this decision was driven by the fact that using a narrower level of detail would have led to over-specification and over-sparsification, eventually compromising the generalization of results. Nonetheless, to build more meaningful models, in the case of events where targtype was equal to “Other”, we have used variable targsubtype instead. In fact, the residual label “Other” includes heterogeneous targets that become more informative if analyzed as separate objects (examples of targsubtype variables are firefighters and ambulance).

Analytic strategy

This section aims at presenting the main concepts behind trails and transition networks that will be used as quantitative framework to analyze patterns of jihadist groups. Furthermore, the second subsection will specifically concentrate on the description of normalized trail similarity (NTS), a coefficient for assessing pairwise similarity across groups in terms of transitions when targets, weapons and combined targets and weapons sequences are taken into account.

From time-agnostic transition networks to time-dependent trails

Given a transition network \(G=(V,E,W_{E})\), with V representing the set of nodes and E being the edges connecting these nodes, the edge weight \(W(v_i \rightarrow v_j)\) can be initially defined as a number related to the edge \(v_i \rightarrow v_j\). This value represents the strength of the connection between nodes \(v_i\) and \(v_j\) and it is usually obtained as a sum of observed directed pairwise connections between them. Specifically, the weight \(W(v_i \rightarrow v_j)\) transforms then into the probability of moving from node \(v_j\) to node \(v_j\). More formally, if an ego at time \(d_k \in D\) is denoted as a random variable \(X_{d_k}\) where X can take any value from the set of nodes V, we can define now the transitional probability of going from node \(v_i\) at time \(d_k\) to node \(v_j\) at time \(d_{k+1}\):
$$\begin{aligned} P\left( X_{d_{k+1}} = v_j | X_{d_k} = v_i\right) = \frac{W\left( v_{i_{d_k}} \rightarrow v_{j_{d_{k+1}}}\right) }{\sum _j W\left( v_{i_{d_{k}}} \rightarrow v_j\right) }. \end{aligned}$$
(1)
Equation (1) shows that the transitional probability is directly proportional to the weight \(W\left( v_{i_{d_k}} \rightarrow v_{j_{d_{k+1}}}\right)\). This Markovian nature of moving through the network mandates that the next step in the network is only dependent on the current node (Fig. 2).
Fig. 2

Sample transition network with transition probabilities between weapons

However, transition networks are cumulative in their nature as we are compacting the entire data, thus excluding the time- or sequence-dependent micro behaviors of the considered groups. This is why, from the ordinary frame of Markov chains and transition networks, we can derive the concept of “network trail”. Network trails are two-mode directed networks in which the behavior of source nodes is temporally ordered with respect to target nodes. Questions such as “How many times have these two entities moved in the same direction?”, “How many times these two entities were in the same place together?”, “Is there a mimicry dynamic between the two entities?” can be answered using trails. Indeed, the application of network trails, and by proxy transition networks, has already proved to be a successful way to compare and analyze the sequences of events, locations or decisions over time. Specifically, trails have been used in health care, biology and scientific co-authorship networks domains [29, 34, 48]. The main focus of such an analysis is to observe an ego’s path over time through a given set of nodes (Fig. 3).
Fig. 3

Two sample trails of different length

Formally, for each group, \(g_{i}\) is given a sequence of terror events \(A _{gi}=\left( a_{1},\ldots ,a_{n} \right)\) and a sequence \(D =\left( d_{1},\ldots ,d_{n} \right)\), representing temporally ordered discrete timestamps. These two sequences are inherently related because the mapping \(f :\, A\rightarrow D\), which connects every event with a unique timestamp, is always verified. Elements in A are ordered based on D, therefore all the events are ordered by the timestamp they are associated with, and this order goes from the most distant to the least distant with reference to the present time.2 Additionally, we define \(\mathfrak {T}=\left\{ t_{1},\ldots ,t_{k} \right\}\) as the set of possible target types and \(\mathfrak {W}=\left\{ w_{1},\ldots ,w_{l} \right\}\) as the set of potential weapons. Within this frame, we can thus formalize an event in the following compact format:
$$\begin{aligned} a_{gi}\left( d,t,w \right) \; \; \; \; 0<t\le 3\; ;\; 0<w\le 4. \end{aligned}$$
(2)
The format above posits that an event plotted by group \(g_{i}\) is abstractly defined as a combination of three elements: the day it occurred (temporal element), the targets that have been attacked and the weapons that have been employed. In fact, each event might have been directed to up to three targets simultaneously and might have been carried out using up to four weapon types as denoted in Eq. (2). If we consider the formal definition of an event, the three types of network trails \(\psi\) we will deal with in the analysis are the following:
  • \(\psi _{g_i}( d,w)\): a time-ordered trail of weapons;

  • \(\psi _{g_i}( d,t)\): a time-ordered trail of targets;

  • \(\psi _{g_i}( d,t,w)\): a time-ordered trail of targets and weapons.

As mentioned above, the fact that each attack may include multiple targets and weapons dramatically increases the possible combinations of selected targets and weapons to include in the analysis. In fact, in the worst-case scenario, Al Qaeda has attacked 24 types of targets during its existence and employed nine types of weapons. To better depict the extremely wide range of possibilities arising from this problem, it is useful to express it applying basic combinatorics. We first deal with the two single-entity types of trails (excluding for the moment \(\psi _{g_i}( d,t,w)\)). In both cases, combinations of multiple objects (up to three in case of targets and four in case of weapons) are possible, repetitions are plausible (therefore have to be considered), and order matters. This means that in a given combination of three targets, we may have two identical targets and a third different one. Additionally, the order in which these targets or weapons is included in the dataset is important, assuming a hierarchic criterion (descending in terms of importance of the specific feature). Thus, two hypothetical combinations of elements (x, y, z) and (y, z, x) have to be treated as different. Applying these rules, and knowing that our combinations can lie in a finite range, for each trail the equations that yields the final number of possible permutations are the following:
$$\begin{aligned} {\text {Perm}}_{\psi _{g_i}(d,w)}= & {} \sum _{r=1}^{4}w^{r}=9+9^{2}+9^{3}+9^{4}=7,380, \end{aligned}$$
(3)
$$\begin{aligned} {\text {Perm}}_{\psi _{g_i}(d,t)}= & {} \sum _{r=1}^{3}t^{r}=24+24^{2}+24^{3}=14{,}424. \end{aligned}$$
(4)
These two equations already highlight the huge amount of possible combinations for the two simplest trails and this already showcases that we need a more practical way to tackle such data. Additionally, the number further increases when considering the third type of trails. Indeed, \(\psi _{g_i}( d,t|w )\) aims at mapping the trajectories of groups’ behavior when targets and weapons are considered together. In this particular case, we are dealing with a simpler probabilistic problem. As an example, we should think as two sets of finite elements \(L=\left\{ l_{1},l_{2},l_{3} \right\}\) and \(M=\left\{ m_{1},m_{2} \right\}\). Our particular problem is finding the number of possible combinations of unique pairs of elements, and it is necessary that each pair contains one element from set A and one element from set B. Thus, we are not interested in finding unique pairs such as \(( l_{2},l_{2} )\) or \(( m_{1},m_{2} )\). Given these constraints, it is straightforward to verify that the number of potential unique pairs in our ad hoc example is given by the product of the number of elements in A and the elements in B. Therefore, going back to the main case:
$${\text {Perm}}_{\psi _{gi}( d,t|w )} = \left( \sum _{r=1}^{3} t^{r} \right) \left( \sum _{r=1}^{4}w^{r} \right) = 14,424 \times 7,380=106,449,120.$$
Applying the calculation to our third trail leads to multiply 14,424 by 7380. The final result is 106,449,120. Considering more than 106 million combinations would have led to a very high expense of computational resource. Additionally, considering all potential combinations might bias the computation of the normalized transition coefficient. Therefore, to simplify this task, we have coded and considered only the combinations (for all trails) existing in the dataset. The only existing rule, indeed, was that that specific combination of targets or weapons was present in at least one of the events of at least one group. The decision of not considering all potential combinations might be contrasted by one’s critique, saying that only considering recorded combinations is a way to artificially bind the extreme wide range of options in the hand of terrorist organizations (especially if considering that the organizations in analyses have—or had—availability of many resources in economic and operational terms). In spite of this, the analysis focuses on the past, hence concentrating on the universe of existing combinations without paying attention to potential future unexplored combinations. This justifies our choice. That considered, applying this reduction led to sensibly smaller numbers. The first trail \(\psi _{g_i}\left( d,w \right)\) is limited to a total of 55 states, \(\psi _{g_i} ( d,t )\) is bounded by a total of 200 states, and \(\psi _{g_i} ( d,t,w )\) has 703 states. In the case of \(\psi _{g_i}( d,w ),\) it means that only 0.71% of weapon combinations have been found in the data, while for \(\psi _{g_i}\left( d,t \right)\) the percentage is 1.38%. Finally, for \(\psi _{g_i}\left( d,t, w \right)\) the number reduces further sensibly: data yields the 0.0006% of total potential combinations of targets and weapons. Table 2 guides the reader in decoding the abbreviations used in the plots and Fig. 4 visually presents the distribution of most common nodes (i.e., combinations) for target, weapons and both combined across each group.
Table 2

List of abbreviations of targets and weapons used in Fig. 4

Abbreviation

Type

Full name

E/B/D

Weapon

Explosives/bombs/dynamite

Fi

Weapon

Firearm

Un

Weapon and target

Unknown

In

Weapon

Incendiary

Me

Weapon

Melee

Po

Target

Police

PC&P

Target

Private citizen and propriety

GG

Target

Government (general)

Bu

Target

Business

Mi

Target

Military

RF/I

Target

Religious figures/institutions

T/NSM

Target

Terrorists/non-state militia

Figure 4 shows how in terms of weapons (first column, in blue), the Islamic State has a sensibly higher preference to the use of explosives/bombings/dynamite (E/B/D) in its attacks. E/B/D accounts for almost 60% of the weapons used in each event. A similar finding is displayed for Al Qaeda, while the Taliban, Boko Haram and Al Shabaab tend to diversify more and to have less stronger preferences. Notably, Boko Haram is the only group that uses more firearms (Fi) than explosives in its attacks.
Fig. 4

Histograms of the five most common states from each of the jihadist groups’ trails

For what concerns targets, the Islamic State again shows a very strong preference for a particular type (i.e., private citizen and property, PC&P). This also applies to Boko Haram. Both groups tend to hit PC&P in almost half of their events. Taliban, Al Shabaab and Al Qaeda exhibit less polarized distributions. It is worth mentioning how the Taliban is the only jihadist organization that prefers to target police rather than PC&P.

Finally, in the combined scenario, distributions of the five most common combinations are more homogeneous for all groups but the Islamic State. In this last case, the group led by al-Baghdadi further demonstrates to have a very clear tendency to hit PC&P using E/B/D (\(\sim\) 30% of attacks). Although with different proportions, this combination is the most common one also for Al Qaeda. Boko Haram and al Shabaab tend instead to target PC&P using firearms, while the Taliban use firearms to attack police.

Normalized trail similarity

Having set up the information framework of the work, we have developed the normalized transition similarity (NTS) coefficient. A transition is a single-step change of state in the ordered sequence of attacks. For example, in the case of time-ordered sequence of targets \(\psi _{g_i}( d,t )\), it is a single-step change in targets group \(g_i\) selected in two sequential attacks. To start to familiarize with the concept of transition similarity, we introduce a simple statistic which only takes into account the absolute frequency of shared transitions between two entities g1 and g2 (i.e., groups, in this specific experiment). This type of computation, for instance, is included in the dynamic network analysis software ORA [7] and is calculated as:.
$$\begin{aligned} {{\text {Tr}}_{\text {common}} }=\; \sum _{i,j} {\text {min}}[ \Phi _{g_{1}}( s_{i}\rightarrow s_{j} ), \Phi _{g_{2}}( s_{i}\rightarrow s_{j} )], \end{aligned}$$
(5)
where \(s_{i}\) and \(s_{j}\) are two distinct generic states and \(\Phi _{g_{k}}\) denotes the number of transitions between states \(s_{i}\) and \(s_{j}\) in the trail of group \(g_k\). Equation (5) gives us the number of common transitions between two trails expressed as the minimum sum of all single link paths (between hypothetical \(s_{i}\) and \(s_{j}\)) shared by two groups. This type of descriptive statistic can be used to evaluate the absolute frequency of shared transitions; however, this statistic can be highly biased when analyzing trails of significantly different dimensions, as in our case (Table 3).
Table 3

Trail length per jihadist group

Group

Trail length

Taliban

5628

Islamic State

3561

Al Qaeda

1501

Al Shabaab

1694

Boko Haram

1900

For instance, when calculating transitions for five groups it is expected that the groups with very long trails will share more common transitions in absolute terms. However, this does not mean that the highly active pair of groups shares more than the other. For this specific reason, we propose a new coefficient of transition which normalizes the absolute frequencies and allows to make pairwise comparisons to evaluate the extent to which each group is similar to another in terms of trail dynamics. This coefficient is calculated as follows:
$$\begin{aligned} {\text {NTS}}\left( g_{1} ,g_{2}\right) =\frac{\; \sum _{i,j} {\min }\left[ \Phi _{g_{1}}\left( s_{i}\rightarrow s_{j} \right) , \Phi _{g_{2}}\left( s_{i}\rightarrow s_{j} \right) \right] }{{\max }\left( |A_{g_{1}}|,|A_{g_{2}}| \right) -1}. \end{aligned}$$
(6)
NTS normalizes the number of times that each entity pair travels the same single link by the number of links of the longest trail in each pair (which is equal to the total number of states minus 1).
Once this coefficient is calculated, to actually rescale values to take into account the relative differences between outcomes of the considered pairs, a further normalization can be performed. So, for groups \(g_{1}\) and \(g_{2},\) the final value would be calculated as:
$$\begin{aligned} {\text {NTS}}\left( g_{1},g_{2} \right) _{\text {scaled}}=\frac{{\text {NTS}}\left( g_{1},g_{2} \right) }{{\max }_{m,n \in G}{\text {NTS}}\left( g_{m},g_{n} \right) }, \end{aligned}$$
(7)
with G representing the set of groups in the analysis (five in our case). To further explain how NTS works, Fig. 5 provides a visual representation of Eqs. (6) and (7).
It is worth mentioning that NTS, while allowing for intra-sample pairwise comparison, cannot be used to compare pairs belonging to different samples. In the case of two sets A and B,  an entity (e.g., a terrorist group) \(g \in A \, \wedge B\), \(NTS(g,x_{A})\) cannot be compared with \(NTS(g,x_{B})\), where \(x_{A}\) and \(x_{B}\) are two given entities belonging to sets A and B.
Fig. 5

Depiction of NTS across three short sequences

Results

This section will showcase and explain the findings of the analysis in the following subsections: one for each trail type, with a conclusive subsection for summing up the main results.

Trails of weapons \(\psi _{g_i}\left( d,w \right)\)

This first family of trails seeks to understand and investigate potential patterns in how groups change their weapons for plotting terrorist attacks. Weapons can be extremely different, and each type of weapon can denote distinct and meaningful aspect of the consequences of an event and of the power, strength and resources of a group. Data show that the number of unique weapons is similar for all groups (ranging from a minimum of 23 to a maximum of 34 combinations). When focusing on unique transitions, the picture slightly changes. In fact, Boko Haram shows nearly double unique transitions with respect to Al Shabaab (188 vs 99), demonstrating how the former group seems less predictable and stable in its operational choices. Finally, the third column further highlights evident differences between groups: the longest identical subsequence of weapons for the IS is significantly longer than the subsequences associated with all the other groups (Table 4).
Table 4

Descriptive statistics of transition networks of weapons per terrorist group

 

N unique weapons combinations

N unique transitions

Longest Id. subsequence

Taliban

34

180

21

Islamic State

33

157

110

Boko Haram

29

188

15

Al Shabaab

23

99

12

Al Qaeda

25

100

30

Table 5 presents the detailed outcomes of the NTS. Al Qaeda and Al Shabaab appear to be the most similar groups according to NTS, while their absolute number of shared transitions was not particularly relevant when looking at the mere sum. Al Shabaab and Boko Haram is the second-most similar pair, while in transition count they were the third less similar pair. Interestingly, Al Shabaab demonstrates a high degree of trail similarity with two different groups. In general, the differences between rankings highlight how NTS calculation sensibly changes the initial results. In terms of ranking (which is a measure that should be handled carefully because we do not control for relative quantitative differences), only one pair remained in the same position. Another finding is that, although they have the longest trails, therefore increasing the relative probability of sharing transitions, the Taliban and the Islamic State are only the fourth most similar pair (0.68).
Table 5

NTS results for weapon trails

Pair

Shared trans (count)

Count rank

NTS

Scaled NTS

NTS rank

Rank diff

Al Qaeda and Al Shabaab

1150

6

0.68

1.00

1

5

Al Shabaab and Boko Haram

1022

8

0.54

0.79

2

6

Al Qaeda and Boko Haram

891

9

0.47

0.69

3

6

Taliban and IS

2585

1

0.46

0.68

4

\(-\) 3

Al Shabaab and IS

1398

3

0.38

0.56

5

\(-\) 2

Taliban and Al Shabaab

1736

2

0.31

0.45

6

\(-\) 4

Al Qaeda and IS

1058

7

0.29

0.43

7

0

Taliban and Boko Haram

1383

4

0.25

0.36

8

\(-\) 4

Boko Haram and IS

836

10

0.23

0.34

9

1

Taliban and Al Qaeda

1212

5

0.22

0.32

10

\(-\) 5

Trails of targets \(\psi _{g_i}( d,t )\)

The second considered trail network regards selected targets. The Taliban, also due to their longer history and sequence of events, shows the highest number of unique targets and transitions. Specifically, in terms of the unique transition case, their total is more than three times the Al Qaeda’s one, which across all groups seems to be more homogeneous, although its event history is the shortest overall (Table 6).
Table 6

Descriptive statistics of transition networks of targets per terrorist group

 

N unique target combinations

N unique transitions

Longest Id. subsequence

Taliban

118

988

26

Islamic State

91

752

99

Boko Haram

65

427

29

Al Shabaab

89

638

11

Al Qaeda

92

301

10

Also in the target scenario, Al Qaeda and Al Shabaab prove to be the most similar groups (Table 7). Stability holds also for the less similar pair, namely the Taliban and Al Qaeda. Conversely, while Boko Haram and the Islamic State differed the most in the previous analyses on weapons, here they are ranked high (fourth position), denoting how, actually, a certain degree of similarity in a specific behavioral dimension does not imply automatically that groups are similar overall. This might suggest how, although employing and applying different methods and resources, both groups seem to have similar strategies with respect to targets. Likewise, while the Taliban and Al Shabaab were not particularly close in terms of single link transitions of weapons, they show high similarity in the choice of new targets.
Table 7

NTS results for target trails

Pair

Shared trans (count)

Count rank

NTS

Scaled NTS

NTS rank

Rank diff

Al Qaeda and Al Shabaab

1011

8

0.60

1.00

1

7

Al Shabaab and Boko Haram

999

9

0.53

0.88

2

7

Taliban and IS

2518

1

0.45

0.75

3

\(-\) 2

Boko Haram and IS

1555

4

0.43

0.71

4

0

Al Qaeda and Boko Haram

763

10

0.40

0.67

5

5

Al Shabaab and IS

1360

6

0.37

0.62

6

0

Taliban and Al Shabaab

1784

2

0.32

0.53

7

\(-\) 5

Al Qaeda and IS

1070

7

0.29

0.49

8

\(-\) 1

Taliban and Boko Haram

1601

3

0.28

0.48

9

\(-\) 6

Taliban and Al Qaeda

1363

5

0.24

0.41

10

\(-\) 5

Trails of targets and weapons \(\psi _{g_i}( d,t,w)\)

The final type of trail analysis integrates both the previous considered dimensions of terror events: weapons and targets. It relies on a much vaster quantity of possible combinations and its nature makes it potentially more informative than the previous two. In terms of basic information, while all sequences of identical combinations diminished in length in this case, the Islamic State is the only one that actually shows a very long sequence (identical to the target one). Overall, conversely, group demonstrated the tendency to change combinations very frequently. Al Shabaab, for instance, has a longest sequence of only four consecutive identical combinations. Secondly, the Taliban (followed by the Islamic State) is again the group with the largest behavioral repertoire, both in terms of unique targets and weapons states and unique transitions (Table 8).
Table 8

Descriptive statistics of transition networks of weapons and targets per terrorist group

 

N Unique Trgt and Wpn combinations

N Unique transitions

Longest Id. subsequence

Taliban

363

2102

20

Islamic State

280

1376

99

Boko Haram

220

1034

14

Al Shabaab

218

1048

4

Al Qaeda

214

896

10

In the combined setting, the Taliban and the Islamic State are found to be the most similar groups (Table 9). Al Qaeda and Al Shabaab, which were ranked first in the previous cases, are now ranked second (while still performing a result almost identical to the highest one). Al Shabaab appears to be very similar also to Boko Haram (third highest NTS value), while the Nigerian group seems to be significantly dissimilar not only to the Taliban but also to the Islamic State. It is interesting to note that the two pairs that yielded the second and third highest results in the NTS computation had actually a very low shared transition count. In terms of extreme dissimilarity, the Taliban and Al Qaeda are detected as the most dissimilar pair also when weapons and targets are considered together.
Table 9

NTS results for target|weapons trails

Pair

Shared trans (count)

Count rank

NTS

Scaled NTS

NTS rank

Rank diff

Taliban and IS

2037

1

0.36

1.00

1

0

Al Qaeda and Al Shabaab

604

9

0.36

0.99

2

7

Al Shabaab and Boko Haram

624

8

0.33

0.91

3

5

Taliban and Al Shabaab

1385

2

0.25

0.68

4

\(-\) 2

Al Shabaab and IS

813

5

0.22

0.62

5

0

Al Qaeda and Boko Haram

405

10

0.21

0.59

6

4

Taliban and Boko Haram

1066

3

0.19

0.52

7

\(-\) 4

Boko Haram and IS

688

6

0.19

0.52

8

\(-\) 2

Al Qaeda and IS

672

7

0.18

0.51

9

\(-\) 2

Taliban and Al Qaeda

999

4

0.18

0.49

10

\(-\) 6

Summary of results

The comparative analysis indicates that the results across trails are generally stable. Indeed, three pairs out of ten perform standard deviation values of ranking lower than one position, as shown by Table 10 and Fig. 6. Particularly, Al Qaeda and Al Shabaab are found to be the most similar groups overall, with a mean rank of 1.33: it is interesting to detect this stable similarity, considering that Al Shabaab officially became part of the Al Qaeda global network in 2012. Al Shabaab and Boko Haram are the second most similar pair. Regarding most dissimilar groups, a certain degree of stability is also shown, especially in the case of the Taliban and Al Qaeda: the pair is always ranked tenth. Little variance is exhibited by the Taliban and Boko Haram and Al Qaeda and the Islamic State. The latter pair deals with two groups that have been referenced by many as the old and the new paradigm of Islamic terrorism in the world, which do not show any evidence of similarity. This may propose that, besides other evident differences that span from the structural organization to the geographic scope of the operations, they also follow distinct behavioral trajectories.
Table 10

Summary of NTS results (R indicates ranking position)

 

Weapon

Target

Target + weapon

Mean R

St. Dev.

Pair

Scaled NTS

NTS rank

Scaled NTS

NTS rank

Scaled NTS

NTS rank

Al Qaeda and Al Shabaab

1.00

1

1.00

1

0.99

2

1.33

0.58

Al Shabaab and Boko Haram

0.79

2

0.88

2

0.91

3

2.33

0.58

Al Qaeda and Boko Haram

0.69

3

0.67

5

0.59

6

4.67

1.53

Taliban and IS

0.68

4

0.75

3

1.00

1

2.67

1.53

Al Shabaab and IS

0.56

5

0.62

6

0.62

5

5.33

0.58

Taliban and Al Shabaab

0.45

6

0.53

7

0.68

4

5.67

1.53

Al Qaeda and IS

0.43

7

0.49

8

0.51

9

8.00

1.00

Taliban and Boko Haram

0.36

8

0.48

9

0.52

7

8.00

1.00

Boko Haram and IS

0.34

9

0.71

4

0.52

8

7.00

2.65

Taliban and Al Qaeda

0.32

10

0.41

10

0.49

10

10.00

0.00

St. Dev

0.22

 

0.19

 

0.20

   
Another relevant case regards Boko Haram and the Islamic State: the Nigerian organization is affiliated to the group led by Abu Bakr al-Baghdadi, but their similarity scores are particularly low. In fact, in the case of weapons and weapons and targets combined, these groups rank among the last positions. However, in the target-only case, these differences vanish. This case is a further proof of the fact that similar strategies of target selection can be coupled with very distinct choices in terms of weapons.
Fig. 6

3D scatter plot of scaled NTS for group pairs (size is scaled by the inverse of the mean R—bigger points mean better mean ranking across trails)

Finally, to ensure that our coefficient is not biased by the skewness of the original length of the time series and the consequent temporal distribution of events, we have performed a sensitivity analysis. This sensitivity analysis has been conducted creating two shorter time series: one taking into account events that happened from January 2007 to December 2016, and the other one considering only events that happened from January 2012 onward. Pearson and Spearman correlation coefficients have been calculated to evaluate the extent to which limiting the time span would affect both the NTS coefficients and the related rankings. Table 11 shows that the results remain stable for all trails in both scenarios, thus suggesting that our initial choice to include all the events present in the dataset has not led to misleading outcomes.
Table 11

Sensitivity test—NTS values and rankings comparison across 2007- and 2012-censored sequences

Trail

2007 censoring \({N}=13{,}794\)

2012 censoring \({N}=11{,}743\)

Pearson’r R

Spearman’s Rho

Pearson’r R

Spearman’s Rho

Weapon

0.98*

0.98*

0.81*

0.86*

Target

0.89*

0.85*

0.84*

0.85*

Target + weapon

0.99*

0.99*

0.92*

0.92*

*Indicates that the coefficient is significant at 99.9% Level

Conclusions and future work

The use of network analysis for knowledge discovery in terrorism research is a well-established practice. Generally, studies in this area focus on a single or few terrorist groups to assess structural properties of organizations and key roles to provide insightful suggestions for potential intelligence and policy interventions. Another stream of research that grew in the last decades has focused on terrorist dynamics in terms of events, putting great attention over terrorist tactics and selected targets, aiming at understanding whether patterns or rationales can be extracted when processing historical data. However, these studies generally treated terrorism “as a whole”, thus facing the risk of losing relevant micro- or macro-level differences in historical trends and dynamics that could have been discovered applying a less general frame to the phenomenon. This work has tried in a way to merge both types of background: in fact, it has used network science not in the ordinary way (mapping relations between actors or individuals), but constructing network trails to calculate and assess similar behavioral patterns within a small sample of jihadist groups, namely the Islamic State, the Taliban, Al Qaeda, Boko Haram and Al Shabaab, thus avoiding including in the analyses too many groups with excessively different backgrounds, histories and aims.

In this study, we have constructed trail networks of temporally ordered sequences of attacks, proposed a novel coefficient, Normalized Transition Similarity, and compared the results of the analyses across groups and trails. NTS evaluates behavioral pairwise similarity of single-link transitions between different states (defined by attacked targets, employed weapons and the combination of the two in each attack). It specifically uses the simple count of common transitions controlled by the potential maximum probability of perfect similarity given two random sequences associated with two considered jihadist organizations. The results showed that, across the three different networks, some stable similarities hold. Particularly, Al Qaeda and Al Shabaab (which are formally affiliated, since the former has become part of the global network in 2012) and Al Shabaab and Boko Haram are respectively ranked as the most similar pairs in two contexts out of three. At the same time, some other pairs confirm to be very dissimilar regardless of the transition networks that are considered. This is especially the case of Al Qaeda and the Taliban. A final interesting result emerges looking at Boko Haram and Islamic State, which are very different when weapons and targets and weapons are considered, but appear to be quite similar when only targets are included in the computation. This may suggest that, regardless of the proposed target, two groups may try to attack using very distinct strategies (in this case, intended as weapons), thus providing potential interpretation on the scale of resources of the considered jihadist organizations.

The relevance of this exploratory analysis lies in the attempt to extract synthetic informative indications from the complex and heterogeneous behavioral dimensions of the most active jihadist groups in the global scenario. While detecting and assessing contextual differences between terror actors is valuable, it is also relevant to investigate how, if and to what extent they are similar to each other, especially when considering “state changes”. Indeed, “state changes” may be fundamental sources of information for researchers and intelligence analysts, because in the frequent and apparently chaotic evolution of these behaviors lie the extreme difficulty of predicting, forecasting and countering terrorism as a violent act.

Although this is an exploratory work, it poses several policy implications. From a practical point of view, similarity measures that take into account dynamic behaviors can be used by analysts to improve profiling of terrorist groups (especially if applying this methodology to larger samples involving higher number of groups) going beyond more static information, regarding for instance ideology, area of action and organizational structure. Furthermore, this general analytic approach can be helpful in designing countering strategies based on recurring sub-sequences or common state changes. Terrorist events can be extremely harmful for societies, but every attack can be very different in scale with respect to a previous or future one. For this reason, it is in the interest of institutions to understand how terrorists change their strategies and tactics. Combining additional information on attack magnitude or effects, trails would be helpful in informing analysts and policy makers on the drivers of terrorist tactical patterns, facilitating alert tools and investigating the nature of successful (or unsuccessful) attack campaigns. With this regard, the trail framework is flexible in highlighting relevant evolution in groups’ behavior, both for single groups and in a comparative fashion. This flexibility can be exploited in different manners, focusing on specific time windows for reducing the noisy effects of events that are distant in time, or concentrating on precise dimensions of terrorist attacks.

Besides the outcomes presented in this article, the study certainly has several limitations, which call for further work that can improve research and policy applications. First, our analyses do not consider the temporal delta that occurs between two events. Given that terrorism naturally clusters in time [46], and that our sequences are long, not taking into account the time that separates two events may lead to biased results that overestimate transition similarity. In fact, it may be useful to break up trails that are more aligned to the temporal elements, considering that two events that are consecutively ordered in the original sequence may be far apart in the temporal scale, and therefore it would be very risky to infer any kind of rational relation between the two events and, even more, between the characteristics of the two.

A second order of limitations comes from the fact that the NTS only considers single-link transitions when one-dimensional transition networks are analyzed. However, to investigate more complex patterns it would be valuable to construct high-dimensional transition networks (including \(2,3,\ldots ,n\) states) to understand how transition matrices change when a wider temporal structure is imposed. Additionally, also NTS should be modified to take into account this new structure of the networks, involving more complex combinatorics.

A third order of limitations is given by the fact that NTS can only assess pairwise similarity, without instead providing a global coefficient that can be applied without normalization to the whole sample, thus making it harder to interpret the results.

A fourth and final order of limitations comes instead from the restricted sample of our analyses. Although working on a limited number of groups can provide more detailed and tailored insights, increasing the number of sequences to work with can control for false-positive patterns that may seem similar only due to the restricted number of pairs.

All these limitations are potentially solvable in the future, and this first exploratory study aims at opening the path toward the use of transition networks for terrorism research, showing the potential of this method that goes beyond the ordinary use cases derived from classic social network analysis.

Footnotes

  1. 1.

    We have created a single “Al Qaeda” group category summing together all the events plotted by the following factions present in the dataset, which are part of the greater Al Qaeda network: Al-Qaida, Al-Qaida in Iraq, Al-Qaida in Saudi Arabia, Al-Qaida in the Arabian Peninsula (AQAP), Al-Qaida in Yemen, Al Qaida in Lebanon, Al-Qaida in the Islamic Maghreb, Al-Qaida in the Indian Subcontinent, Islambouli Brigades of Al-Qaida, Secret Organization of Al-Qaida in Europe, Al-Qaida Organization for Jihad in Sweden, Al-Qaida Network for Southwestern Khulna Division, Jadid Al-Qaida Banglades (JAQB), Al-Qaida Kurdish Battalions.

  2. 2.

    It is worth specifying that in the analyses, events will be ordered temporally but without taking into account the actual delta between attacks. This means that there is no difference between two attacks plotted within a range of 4 days and the other two attacks plotted within a range of 5 months. Additionally, when two or more attacks are plotted on the same day, we order them by the eventid variable included in the original dataset, assuming that the information coded in the variable provides a more robust ordering criterion than pure random distribution.

Notes

Acknowledgements

The authors would like to thank the two anonymous reviewers for their comments on a previous version of the paper. This work was supported in part by the Office of Naval Research under the Multidisciplinary University Research Initiatives (MURI) Program award number N000141712675, Near Real Time Assessment of Emergent Complex Systems of Confederates, the Minerva program under grant number N000141512797, Dynamic Statistical Network Informatics, and by the center for Computational Analysis of Social and Organizational Systems (CASOS). The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the ONR or the US government.

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Transcrime-Università Cattolica del Sacro CuoreMilanItaly
  2. 2.Carnegie Mellon University, CASOSPittsburghUSA

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