Introduction

Disrupting criminal networks is one of the main promises of applying social network analysis (SNA) to criminology and criminal investigation. Several studies have investigated resilience of criminal networks and the effect of various types of disruption on network structure, such as the removal of central actors or actors with specific skills (Bright, 2015; Carley et al., 2002; Wood, 2017). While maximizing the potential of a disruption strategy may be helpful in incapacitating the targeted network, usually the network does not cease to exist. Instead, the actors who remain in the network respond to the disruption, and as a result, the network structure may recover to an extent. It is this response of actors to disruption and subsequent recovery of the network that have been acknowledged in the recent research on criminal networks (Berlusconi, 2022; Duijn et al., 2014; Duxbury & Haynie, 2019, 2020). This is especially important considering the fact that interventions against criminal networks may trigger negative unintended consequences in the form of strengthening network cohesion (Diviák et al., 2022; Duijn et al., 2014) which may make the network more efficient, adaptable, or dangerous.

This study aims to build on this recent stream of research by using a real-world street gang network (Grund & Densley, 2012, 2014) as a basis for simulating the effect of disruption and subsequent recovery on its structure. The purpose of this research is twofold. The first goal is to analyse the empirical network and simulate appropriate disruption strategies and their immediate impact on the structure of the network. The second goal is to simulate hypothetical response of actors remaining in the network and the conditions under which the disrupted network recovers or disintegrates. The study is therefore not a guide nor an empirical prediction of the network’s evolution but rather an artificial demonstration of potential short- and long-term consequences of criminal network disruption. The ultimate message of the present study is that even well-designed and carried-out disruptions and interventions may bring about consequences that may hinder or reverse their intended effect, such as when targeted networks become more radicalised, cohesive, or efficient as a result of the recovery (cf. Diviák et al., 2022; Duijn et al., 2014; Morselli & Petit, 2007).

The study follows a somewhat unusual four-stage design in which each stage contains its own theory and methodology, and each stage follows from the results obtained in the previous stages. Therefore, this study is structured to reflect the four stages with all the necessary information relevant for theory, methods, and results contained in the corresponding sections. The final discussion brings all the sections together with practical implications of this study and their methodological and ethical ramifications.

The first stage consists of a descriptive analysis which maps the structure and cohesion of a street gang network. The second stage identifies the relational mechanisms that affect the formation of ties in the network using a stationary stochastic actor-oriented model. In the third stage, nine different disruption strategies are formulated based on previous research and results from stage 1, and their effects on the network’s structure are subsequently simulated. In the fourth and final stage, the disrupted networks which result from each of the nine disruptions in stage 3 are allowed to recover by simulating their evolution using the stochastic actor-oriented model and varying the parameter values obtained in stage 2.

Criminal network analysis and network simulation

Given the interest of criminology and criminal investigation in designing evidence-based disruption strategies, it is not surprising that there are a number of articles studying disruption of criminal networks. There are two main types of these studies. On the one hand, there are observational studies describing how a specific disruption affected the studied network (e.g. Berlusconi, 2022; Diviák et al., 2022; Morselli & Petit, 2007). On the other hand, there are simulation studies assessing what may be the most efficient hypothetical disruption strategy for a given network (e.g. Bright, 2015; Carley et al., 2002; Morselli & Roy, 2008; Wood, 2017). However, both lines of inquiry face problems when it comes to assessing the effect of criminal network disruption. The problem with observational studies is that it is usually impossible to distinguish the causal effect of the disruption from the effects of confounding internal or environmental factors. The problem with simulation studies usually lies in their sole focus on the immediate impact of the disruption, disregarding the response of actors who remain in the network and its long-term consequences.

Agent-based modelling is a set of computational methods simulating the interactions between agents and their environment (ABM; Calderoni et al., 2022; Gilbert, 2008). Simulation studies using ABM can bridge this gap by allowing researchers to simulate virtual experiments in a controlled setting, enabling isolation of the effects of specific disruption strategies and recovery scenarios. Such control is difficult or outright impossible to achieve in real-world settings due to both methodological and ethical limitations. Duxbury and Haynie (2019) used empirical data about four criminal networks in an ABM to simulate the effect of removing central actors and subsequently to simulate how fast the networks would recover. In another study, Duxbury and Haynie (2020) analysed a large bipartite network of buyers and vendors on an online marketplace and used model estimates to inform their ABM simulations of actors’ response to disruption attempts. In a similar vein, Duijn and colleagues (2014) simulated human and social capital disruption in a cannabis cultivation network and its capacity to recover by using algorithms that change the structure of ties in the network. All these studies show remarkable capacity of criminal networks and their members to withstand and adapt to disruption.

The drawback of simulation studies is their artificiality, as they are built upon assumptions that may have limited validity beyond the given simulation setting. The abovementioned studies used real-world data and calibrated their simulations accordingly. This study follows a similar logic by using the information about the structure and mechanisms driving formation of ties in a real-world criminal network. This information is then used for simulating disruption strategies that are meaningful for the given network, and also to simulate the response of actors using parameter values describing their tendencies to form ties. While such an approach reduces artificiality, it does not entirely remove it. The simulations here in effect portray how the actors in the networks might respond based on their observed tendencies and how that may affect the structure of the network as a result. This assumes that all actors probabilistically follow the simulated recovery scenario and that there are no other influences affecting the behaviour of actors or the network as a whole. Moreover, since the simulations are calibrated with specific empirical data, their results do not straightforwardly generalise beyond the given case.

The benefit of simulation studies, such as those employing ABM and similar approaches, is their ability to investigate the micro–macro link (Calderoni et al., 2022; Snijders & Steglich, 2015), that is the interplay between micro-level actor behaviour and its macro-level consequences. In this particular case, the micro-level is represented by relational mechanisms, i.e. the tendencies of actors to form their ties in specific patterns, while the macro-level is the emergent network structure. This logic is in line with previous studies investigating the effect of micro-level mechanisms on the overall network structure (Bright et al., 2018; Diviák et al., 2019, 2022; Grund & Densley, 2014; Ouellet et al., 2017). This approach is also consistent with the assumption that ties in the network are sufficient for formation of other ties and thus the emergence of the overall network structure (known as network self-organisation; Robins, 2015) without requiring further assumptions about central or exogenous coordination of the network, as even in highly hierarchical or organised settings (such as legal organisations and companies), the extent of such organisation is only partial at best (cf. Robins, 2015).

Stage 1—network structure

The network data in this study was originally collected and analysed by Grund and Densley (2014). It is a network of a durable street gang with a name, symbols, and other group identity characteristics originating in an impoverished borough in inner London, thereby corresponding to the definition of Eurogang (Grund & Densley, 2012). As such, the network represents a case which may occur in other countries. Moreover, the data is based on detailed police records validated by a fieldwork with the gang members (actors), thus constituting a dataset with not only the ties (defined here as the two actors having committed an offence together at least once in the past) but also with important actor attributes. Together with public availability of the dataset through the covert networks database of Mitchell Centre for SNA (2023), this allows for a more realistic modelling and simulation as well as re-analysis.

The goal of the first stage of this study is to describe the network and its structure and to identify potential targets for the subsequent disruptions. Sociogram (Fig. 1) displays the street gang network, and Table 1 summarises the whole network measures calculated in the igraph package in R (Csardi & Nepusz, 2006) which characterise its structure (for details on these measures, see, e.g. Borgatti et al., 2022; Robins, 2015). The network is composed of 54 actors, with 315 ties among them, resulting in a density of 0.22, which means that 22% of all possible ties are actually present in the network (with 11.67 ties per actor on average). The network exhibits moderate centralisation of 0.25, indicating that the network is reaching 25% of its maximum possible concentration of ties around the most central actor. There are also relatively short geodesic distances (2.05 on average), with the diameter of 4, suggesting that, on average, the actors in the network can reach each other via short paths through one intermediary. The value of the global clustering coefficient (0.52) points towards considerable clustering in the network as 52% of connected triplets are in fact triangles. Taken together, these findings indicate that the network is well-connected and cohesive, which may make it resilient to disruption.

Fig. 1
figure 1

The original network with 54 actors based on Grund’s and Densley’s studies (2014; 2016). Node size relates to their betweenness centrality, while node colour refers to their rank in the gang hierarchy (red = top tier, blue = 2nd tier, green = 3rd tier, purple = 4th tier, orange = bottom tier)

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Table 1 Whole network descriptive measures
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The appendix provides basic descriptive statistics of actors’ attributes. These attributes were also used in further statistical modelling and simulations in stages 2 to 4. The age of the actors ranges from 16 to 27 with an average of 19.83. The number of arrests displays some dispersion as some actors have no experience with being arrested, but there are also actors who have been arrested more than twenty times. Forty-four percent of actors in the network have been imprisoned. The most frequent ethnic group (operationalised as place of birth) in the network is British (born in the UK) with 24 members, whereas there are only six actors with Somali background. As for the ranking within the gang hierarchy, the original research identified five ranks and assigned each actor into one. The top rank is occupied by only a single actor, with more than half of members occupying ranks 3 and 4. Ranking is strongly correlated to actor centrality measures (degree, betweenness, eigenvector centrality, see stage 3; Spearman’s ρ > 0.7 in each case).

Stage 2—relational mechanisms

In stage 2, the relational mechanisms underlying tie formation in the network are identified, and subsequently, this knowledge is used to empirically calibrate the simulations in stage 4. In order to identify which relational mechanisms are driving the formation of ties in the network, a stationary stochastic actor-oriented model (SAOM) was fitted to the data using the RSiena package in R (Ripley et al., 2019). A SAOM aims to capture the mechanisms that drive evolution of a network over time using network panel data (Snijders, 1996; Snijders et al., 2010). Essentially, SAOM models the evolution of the network as a series of micro-steps, wherein each actor has the opportunity to change their ties. The SAOM consists of two components: rate function, which models how often the actors get the chance to change their ties, and the substantively more interesting objective function, which models how specified relational mechanisms affect this change. Stationary SAOM (sSAOM; Snijders & Steglich, 2015) is a modification that can be used to model cross-sectional data by fixing the rate function. The results of sSAOM then indicate what mechanisms keep the network in its current state (for details on SAOM, see the Appendix).

The model specification is based on distinguishing the mechanisms into trust-enhancing and risk-reducing mechanisms (Diviák et al., 2022). The effect of trust-enhancing mechanisms on tie formation in the network is expected to be positive, because these mechanisms are related to network microstructures facilitating and bolstering trust, cooperation, and control between the actors in accord with previous research on criminal networks (Bright et al., 2018; Diviák et al., 2019; Ouellet et al., 2017). The trust-enhancing mechanisms investigated in this study are triadic closure and homophily on age, ethnicity, and rank within the gang’s hierarchy. Risk-reducing mechanisms are expected to have negative effect on tie formation as they are related to configurations of ties that increase visibility of actors, which they are generally assumed to avoid in criminal networks (Bright et al., 2018; Diviák et al., 2019; Ouellet et al., 2017). Risk-reducing mechanisms in this study are tie accumulation, brokerage, and activity based on age, and previous arrest or prison experience.

Table 2 shows the results of the stationary SAOM. The results in Table 2 are based on a model with adequately converged estimates. Positive estimates indicate that actors tend to prefer to form ties that are part of the structures represented by a given effect, whereas negative estimates indicate that actors tend to avoid forming ties in such configurations. These particular results were obtained using the forcing algorithm, but they are not substantially different from the model results obtained with the unilateral initiative and reciprocal confirmation model, suggesting robustness of the parameter estimates to the choice of estimation algorithm (additional results and details about these algorithms can also be found in the Appendix). The goodness of fit of the model to the data was assessed by inspecting to what extent the model can recreate three whole network properties of the network: degree distribution, geodesic distances distribution, and triad census. The model shows adequate fit on all these properties (results listed in the Appendix).

Table 2 Stationary stochastic actor-oriented model results. Statistically significant effects are in bold
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From among the trust-enhancing mechanisms, three display statistically significant effects. The largest overall parameter is GWESP (geometrically weighted edge-wise shared partner; Snijders et al., 2006) that captures triadic closure. The positive estimate indicates that actors in the network display strong tendencies toward closing open triangles, i.e. actors tend to cooperate with those they share common co-offenders with. Both remaining trust-enhancing mechanisms with statistically significant effects pertain to homophily, in one case on age and in the other on ethnicity. Both these effects are positive, which suggest that actors in the network have tendencies to co-offend with those who are similar to them in terms of age or ethnicity.

As for the risk-reducing mechanisms, our model found two statistically significant effects. The first effect is the degree act + pop effect, which operationalises tie accumulation. The parameter estimate is rather small, indicating that actors in the network have weak tendencies towards proliferating their ties, i.e. those who have a lot of criminal collaborators tend to co-offend even more. The betweenness effect, capturing the mechanism of brokerage, is negative, suggesting that actors tend to avoid positioning themselves between other actors.

Stage 3—disruption strategies

Stage 3 investigates the immediate effect of disruption on network structure by simulating various node removal strategies. To capture the effect of the simulated disruption strategies on network structure and its recovery, compactness was chosen as a dependent variable in stages 3 and 4. Compactness is defined as the average of reciprocal geodesic distances (Borgatti et al., 2022: 204). Networks with many nodes connected via short distances have compactness values close to 1, whereas disconnected networks or networks with long paths between nodes have compactness closer to 0. Compactness was chosen because it simultaneously captures connectedness of the network (i.e. the extent to which there are paths between actors) and the distances between actors (i.e. how long the paths are). Thus, decreasing compactness indicates that the network is becoming less cohesive and therefore it is more difficult for the actors to cooperate and reach their goals. In order to assure comparability across the disrupted networks which vary in size due to different number of removed actors, the reciprocal geodesic distances are averaged over the number of dyads in the initial undisrupted network, i.e. n = 54 for all the calculations in the following formula.

$$compactness=\frac{\sum_{i\ne j} (\frac{1}{{d}_{ij}})}{n(n-1)}$$

where dij is the length of the geodesic path between actors i and j.

In total, nine proposed disruption strategies which reflect both previous research (cf. Bright, 2015; Duijn et al., 2014) as well as the fact that the network is a concrete gang with its structure (cf. Grund & Densley, 2012, 2014) are simulated:

  • Central actors (5 strategies)—Five strategies target the most central actors according to either degree or betweenness: removing the highest degree and betweenness actor (the same actor in both measures), removing the three and the five highest degree actors, and removing the three and the five highest betweenness centrality actors. Degree is the number of ties a node has and thus captures that node’s direct connectivity, whereas betweenness centrality captures indirect connectivity as it is the number of dyads between which a node is on a geodesic path, thus acting as a broker (Freeman, 1979). The central actor removal simulates the scenarios where law enforcement targets the most prominent actors who may either be highly (inter)active in the network (degree) or hold key brokerage or gatekeeping positions (Bright, 2015; Duijn et al., 2014; Duxbury & Haynie, 2019).

  • Marginal actors (3 strategies)—There are also three disruption strategies targeting the five, eight, and eleven lowest-ranking actors in both degree and betweenness (the same actors on both measures). These disruption strategies capture situations in which highly central figures may be difficult to remove due to their higher sophistication or increased ability to avoid detection. As a result, a higher number of marginal actors may instead be targeted in an attempt to disrupt low-level criminal activity (cf. Duxbury & Haynie, 2020).

  • Gang hierarchy (1 strategy)—Lastly, to account for the gang’s intrinsic hierarchy, there is a strategy targeting the seven actors in the top two hierarchical tiers (the highest tier is represented by only one actor who is coincidentally also the highest degree and betweenness actor, thus removing the highest tier is already included). This strategy corresponds to real-world cases where law enforcement relies on non-network indicators of actor importance or criminal capital (Bright, 2015; Duijn et al., 2014).

Figure 2 captures the effect of the nine disruption strategies on the compactness of the observed network. The value of compactness in the observed network is represented by the red horizontal line in Fig. 2. In general, network compactness decreases with the number of removed actors and their centrality. The removal of the most central actor is the least disruptive strategy whereas removing the seven actors who occupy the top two ranks of the gang’s hierarchy decreases the compactness of the network the most.

Fig. 2
figure 2

Effect of each disruption strategy on standardised compactness. Red horizontal line represents the baseline value of compactness in the observed network

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Stage 4—recovery scenarios

The fourth and final stage consists of simulating the effects of likely actor responses after the disruption. This stage therefore builds on stages 2 and 3. Specifically, each of the nine networks resulting from the disruptions in stage 3 was taken and used for the actor-oriented model from stage 2 to simulate a distribution of 1000 networks. To obtain a baseline scenario, no parameter values from the sSAOM in stage 2 were modified. However, previous research suggests that actors in a network affected by disruption may respond to it by changing their behaviour (Berlusconi, 2022; Diviák et al., 2022; Duijn et al., 2014). To capture this change in the way actors form ties in response to disruption, the five statistically significant effects detected in stage 2 were further modified. The parameter values of the three significant trust-enhancing mechanisms (triadic closure and homophily on age and ethnicity) were increased by 1 (by 0.5 as well for sensitivity analysis; see the Appendix) representing recovery scenarios in which the actors are further motivated to rely on ties embedded in configurations that foster trust and support, and mitigate defection. The parameter values of the two statistically significant risk-reducing mechanisms (preferential attachment and brokerage) were analogously decreased to represent the scenarios in which actors aim to minimise the risk of detection and subsequent arrest by decreasing their visibility. Furthermore, each recovery was simulated with a rate function of 2 representing short-term recovery by essentially giving the actors on average two opportunities to change their ties. To capture the long-term effect, each recovery scenario was also simulated with rate function of 8, a value based on the average number of opportunities corresponding roughly to a year of time in the previous studies using SAOM (Bright et al., 2018; Diviák et al., 2022). Thus, there are six recovery scenarios (baseline + increase/decrease of the five mechanisms) in two temporal regimes (short- and long-term recovery) totalling twelve sets of simulation results. Note that no new actors join the network during the recovery to replace the actors removed by the disruption, because the data does not contain any information about how many and which actors would join, which makes it impossible to empirically calibrate these parameters. Thus, network recovery is guided by the response of the actors remaining in the network after disruption (cf. Calderoni et al., 2022; Duxbury & Haynie, 2019).

The violin plots in Fig. 3 represent the distributions of 1000 standardised compactness values from networks simulated for each of the disruption strategies in stage 3 for the baseline recovery scenario, i.e. the scenario where no parameter values were altered in the model obtained in stage 2. The figure on top captures the short-term recovery while the figure in the bottom captures the long-term recovery. The remaining violin plots for each substantive scenario can be read in the same way. Since no parameter values were altered for this baseline scenario, this set of simulations serves as a control group as well as a ‘sanity check’—the distributions for both short- and long-term recovery follow the pattern in Fig. 2, that is the baseline scenario on average reproduces the immediate effect of each disruption, with compactness being slightly higher in the long-term case due to more opportunities for network actors to form ties.

Fig. 3
figure 3

Recovery of the network—baseline scenario. Top figure = short-term recovery, bottom figure = long-term recovery. Red dashed horizontal line represents the baseline value of compactness in the observed network

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Figure 4 captures the recovery by increasing the effect of homophily on age. Thus, this scenario models what could happen if the disruption incentivised actors to be more likely to form ties with other actors of a similar age. Neither short-term nor long-term recovery is sufficient in this scenario to recover the structure of the network to its baseline level of compactness regardless of the specific disruption strategy. In terms of increasing homophily on ethnicity (Fig. 5), the results are quite similar to the increasing homophily on age scenario. The response of increasing ethnic homophily is not strong enough to allow the network to fully recover in either the short or long term. There is only one exception—the network resulting from removing the one most central actor (‘gang boss’) gets on average almost to the pre-disruption value of compactness in the long-term recovery.

Fig. 4
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Recovery of the network—homophily on age increase scenario

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Fig. 5
figure 5

Recovery of the network—homophily on ethnicity increase scenario

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Recovery by increasing triadic closure, the strongest mechanism identified in stage 2, shows more interesting results depicted in Fig. 6. Already in the short-term recovery we see greater compactness recovery across the disrupted networks, with the most central actor removed network almost reaching the pre-disruption compactness value. Giving the actors in the networks more opportunities to form ties in the long-term recovery results in substantial increases in compactness, which in four of the nine disrupted networks yield recovery of compactness to its initial value or even higher (notably in the cases of disruption by removing up to three of the most central actors). In these cases, we actually see that the increase in the tendency to close open triads can realistically make the network even more compact than it was before the disruption, exemplifying the conditions under which interventions against criminal networks trigger negative unintended consequences. In the four disrupted networks, this recovery scenario undermines the intended effect the disruption in weakening the cohesion of the network by strengthening it instead.

Fig. 6
figure 6

Recovery of the network—triadic closure increase scenario

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Figures 7 and 8 depict the two recovery scenarios in which parameter values were decreased to simulate attempts of actors to reduce the risk of detection by decreasing their criminal collaboration and thus their visibility. Figure 7 specifically captures what could happen if the actors responded to the disruption by avoiding high brokerage positions, represented by the decrease in the betweenness effect. In the short term, there is some decrease in compactness of the network across all the disrupted networks, which is even more pronounced in the long-term recovery. None of the networks resulting from the disruption entirely disintegrates in the recovery by decreasing brokerage though. The opposite is true for the scenario in which actors are incentivised against accumulation of ties, operationalised by decreasing the degree activity and popularity effect related to the preferential attachment mechanism. As Fig. 8 shows, there is already a considerable drop in compactness in the short-term recovery by decreasing preferential attachment, but the long-term case shows complete disintegration of the network structure (near-zero values of compactness) across all the nine disrupted networks. In this case, the response mechanisms triggered by the disruption are actually synergistic with the aim of the disruption as they further perpetuate the dismantlement of the network regardless of what the initial disruption strategy was.

Fig. 7
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Recovery of the network—brokerage decrease scenario

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Fig. 8
figure 8

Recovery of the network—preferential attachment decrease scenario

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As for the sensitivity analysis, the parameter values were also increased or decreased in the recovery scenarios by 0.5 and the same set of simulations were carried out. The results are very similar to those presented here in terms of short-term recovery in all the recovery scenarios. In the long-term recovery, the results aim in the same direction for all the scenarios, but with overall less-pronounced effects and so the recovery is not as strong for triadic closure if the GWESP effect is increased only by 0.5, but the networks still disintegrate despite the smaller decrease in preferential attachment. Therefore, the results presented here can be seen as consistent even for cases where the mechanisms driving recovery are weaker.

Discussion

Overall, the results of this study can be summarised as follows. In terms of the structure of the network and the mechanisms underlying the formation of ties, our results suggest that triadic closure and homophily (on age and ethnicity) play an important positive role in line with previous findings of other studies (Bright et al., 2018; Diviák et al., 2019, 2022) as well as with the studies originally studying the network here (Grund & Densley, 2012, 2014). In terms of the immediate impact of disruption strategies on compactness of the network, we see some variance between the tested disruption strategies, with those that target a higher number of actors or more central actors being more impactful, which is a finding supporting previous research (Bright, 2015; Carley et al., 2002; Duijn et al., 2014; Wood, 2017).

In terms of actors’ response and subsequent network recovery, our results for the short-term recovery do not clearly indicate any particularly noteworthy effect of any of the studied mechanisms. However, long-term recovery is sufficient to demonstrate under which conditions the network recovers or falls apart. The recovery can be seen in the scenarios where the strongest mechanism, triadic closure, is increased. In this case, there are disruption strategies from which the network recovers to its initial compactness values or even exceeds them, which may be understood as a manifestation of a negative unintended consequence of the disruption. Conversely, when the simulated response of actors stimulates their avoidance to accumulate ties (negative preferential attachment), the network nearly or completely disintegrates regardless of the disruption strategy it was subjected to. These results are on the one hand in line with previous simulation studies analysing criminal network recovery that show the capacity of criminal networks to recover or even become more cohesive after a disruption (Duijn et al., 2014; Duxbury & Haynie, 2019, 2020), especially when already strong mechanisms are bolstered further. On the other hand, these results also complement previous research by showing what recovery scenarios may propel network disintegration.

Given the variance in immediate impact of disruption on the network and given the range of outcomes following the recovery after the disruption, the simulations suggest that the mechanisms driving the recovery are at least as important as the disruption strategies themselves. This is an important conclusion because it has three interrelated implications. Firstly, considering only the immediate impact of any disruption attempt is short-sighted as it ignores the range of possible recovery scenarios. Secondly, even in constrained artificial simulation settings, the recovery may hinder or perpetuate the effect of disruption depending on which mechanism drives actors’ response. Hence, inferential network analysis with a model capable of identifying key mechanisms underlying tie formation in a given network should always accompany detailed descriptive accounts. Thirdly, when designing and implementing disruption or more broadly intervention measures for criminal networks, researchers and practitioners alike should not only consider current structure and immediate impact of disruption, but also the response it is likely to trigger and its long-term consequences. This calls for a more integrated thinking about interventions in a broader theoretical, ethical, and practical terms while accounting for all the available qualitative and quantitative information about a given case.

The literature on network interventions (Robins et al., 2023; Valente, 2012) can be of help in further developing this line of research. While Valente (2012) proposes a taxonomy of network interventions in general settings, Robins et al. (2023) build up on Valente’s framework by emphasising the importance of the goal of the intervention and the level at which the intervention operates in the network (individual, setting, or the entire system). In criminal network interventions as in this study, the goal is usually to dismantle the structure of the network so that the capacity of its members to perpetrate crime is reduced. Yet, dismantling the network may not necessarily be the only way to achieve this goal. In some networks, the connections among the actors may not be criminal by nature, but certain behaviours or attitudes spreading on the network may be which is likely to render a network disruption inefficient at best. The disruption strategies tested in this study could all be subsumed under the kinetic approaches to disruption of criminal networks, that is strategies that directly affect the structure of the network (Roberts & Everton, 2011). In the light of a broader approach to criminal network interventions, non-kinetic strategies should be considered as well. Non-kinetic strategies are those that indirectly affect the network by altering the environment in which the network operates or the willingness of actors to continue in criminal activity (cf. Roberts & Everton, 2011). In the cases where involvement in criminal networks provide the most beneficial way to earn sufficient income, arresting or otherwise incapacitating even a high number of actors is not likely to succeed as the primary motivation for criminal involvement remains intact. Non-kinetic approaches in these cases may be far more efficient in providing meaningful alternatives for generating income to mafia networks or for socialising to youth gangs. Testing the effect of such non-kinetic approaches is beyond the scope of network simulations employed in this study, because these strategies by definition affect the network indirectly. Future research could explore the potential contribution of using fully developed agent-based models that allow to not only capture the actors and their ties, but also the resources at their disposal or properties of the environment in which they operate. In a similar vein, an extension to a full ABM or availability of data on actors joining or leaving criminal networks over time could open an avenue for investigating the processes related to recruitment or disengagement that form a major factor in criminal network evolution and adaptation (cf. Calderoni et al., 2022).

The conclusions drawn in the preceding paragraphs are necessarily limited by methodological limitations of the approach taken in this study. Since the simulation results inherently reflect the assumptions on which the simulations were based, they can only be considered as suggestive of certain outcomes rather predictive, i.e. demonstrating what are the consequences of a specific ‘thought experiment’ rather than forecasting future evolution. Realism is limited due to a degree of arbitrariness in some of the choices for parameter values (manipulating the estimate values or setting up rate function values) or the overall design of simulations. Additionally, while calibrating the simulations with empirical data helps in achieving more realistic simulations, the specific results are impossible to generalise to different empirical cases. Lastly, while a similar approach is in principle practically applicable, the success of its application in practice crucially depends on validity and availability of data, which may be problematic in ‘live’ cases where the information is likely to be incomplete or biased and difficult to triangulate and validate.

The use of rigorous methods including SNA turned out to be vital in not only understanding organised crime and co-offending, but also in formulating evidence-based interventions and policies. As this study shows, using network insights does not automatically guarantee a successful intervention, as even for carefully planned interventions there is a risk that the response of actors in the disrupted network brings about unintended consequences that may substantially alter the intended effects of the intervention or outright reverse them. Both researchers and practitioners should therefore exercise caution when designing intervention strategies and especially consider how they may backfire and what that would mean for the actors inside as well as outside of the network.