Corruption is a phenomenon that occurs within the intricate structure of social, political and technological systems, therefore, a better understanding of it requires of integral and inter-disciplinary perspectives. As with contemporary medicine or biology advances, which stand upon the progress made by disciplines such as physics, applied mathematics and computing science, social sciences have begun to use such disciplines to describe, model, explain, and even predict certain phenomena (Conte et al.,
2012; Holme & Liljeros,
2015; Lagi, Bar-Yam, Bertrand & Bar-Yam,
2015; Wiesner et al.,
2018; Capraro & Perc,
2018). This integration of disciplines previously considered totally apart from each other (natural and social sciences, and even the humanities) has been possible due to important advances in computing capabilities, knowledge-transfer and cross-disciplinary problem solving (Ball,
2003; Miller & Page,
2009; Caldarelli, Wolf & Moreno,
2018).
Moreover, in the scientific exploration of physical to social systems, it has been found that the hardest adaptive systems to model and control are those involving individuals whose willing decisions may give rise to collective phenomena that are not easily defined, explained or predicted by means of the analysis of isolated individuals (Ball,
2003; Miller & Page,
2009; Caldarelli et al.,
2018; Capraro & Perc,
2018). In this context, corruption could be regarded as a phenomenon that occurs within systems whose structure and dynamics can evolve as a response to changes in its corresponding socio-political and regulation context, with a strong dependence on the interrelation of different factors and actors acting as a whole. In general, systems with the previous characteristics are the subject matter of complexity or complex systems science, which represents a new scientific paradigm and a new way of doing science in the twenty-first century (Mitchell,
2009; Thurner et al.,
2018; De Domenico et al.,
2019; Helbing et al.,
2015).
Complex phenomena
In complex systems theory, a system is considered complex not only because it has an intricate structure, but also because its temporal evolution cannot be easily explained as a function of the behavior of its isolated components (Bar-Yam,
1997; De Domenico et al.,
2019). In particular, there are two important concepts that help to explain the ‘complexity’ of a system, those are ‘emergence’ and ‘self-organization’ (Sayama,
2015). On the one hand, ‘emergence’ is a concept associated to the effects of non-trivial interrelations among the components of a system across different scales of observation or analysis. Specifically, the properties of the parts acting as a whole are called ‘emergent’ when they cannot be explained based on the properties of the parts looked in isolation, thus, global properties are different from local ones (Bar-Yam,
1997; Sayama,
2015). On the other hand, ‘self-organization’ is a dynamic or temporal process through which the solely interactions among the multiple parts of the system create collective structures and behaviors, with no intervention from a central or external organizing agent (Sayama,
2015). From these concepts, it becomes clear that there are two important aspects to be considered within the analysis of complex systems: the structure (statics) and temporal evolution (dynamics) of the system. In complexity science, network theory is one of the most important tools for the analysis of these structural and dynamical elements (Sayama,
2015; Thurner et al.,
2018).
Complex networks
Network theory has been applied to have a better understanding of many natural, socio-technical, and legal systems (Barabási,
2016; Rutherford, Lupu, Cebrian, Rahwan, LeVeck & Garcia-Herranz,
2018). The importance of the application of multidisciplinary and scientific approaches such as complex systems, network theory, and even physics, to the study of criminal activities was presented by the end of last century (Sparrow,
1991). However, it was until the last decades that these types of studies have begun to gain momentum given the great progress in computing and data science (Caldarelli et al.,
2018) and their enormous relevance in modern social, economic, and political contexts (D’Orsogna & Perc,
2015; Helbing et al.,
2015; Espinal-Enríquez & Larralde,
2015; Marshak, Rombach, Bertozzi & D’Orsogna,
2016; DellaPosta,
2017; Fazekas, Skuhrovec & Wachs,
2017; Morselli & Boivin,
2017; Altshuler & Pentland,
2018; Magliocca et al.,
2019; Ouellet, Bouchard & Charette,
2019; Niu, Elsisy, Derzsy, & Szymanski,
2019).
Notably, although corruption studies go back a long way and have been conducted from different perspectives, corruption studies conducted from a complex systems or network theory approaches are quite recent and scarce. For instance, a recent study covering 30 years of corruption in Brazil shows that the co-occurrence of politicians in corruption scandals create networks with large connected components that might spans decades (Ribeiro, Alves, Martins, Lenzi & Perc,
2018). Other study proposes diverse methods for the strategic dismantling of corruption or crime networks considering their structure and the cost of removing key nodes (Ren, Gleinig, Helbing & Antulov-Fantulin,
2019). Another study looks into the social fabric of Hungary in order to establish the social factors associated to corruption risk in public procurement, finding that fragmented social networks are more prone to corruption risk whilst more diversity hinders it (Wachs, Yasseri, Lengyel & Kertész,
2019). An additional study that explores 28 years of bill-voting in Brazil shows that the dynamics of co-occurrence networks of similar-voting congressmen reveal patterns that allow for the identification of convicted corrupt politicians and also, for the possibility of predicting or identifying other possible corrupt individuals within the network (Colliri & Zhao,
2019). Noteworthy, the identification of latent criminal groups (Campedelli, Cruickshank & Carley,
2019) and the effective dismantling of their organizational structure (Wandelt, Sun, Feng, Zanin & Havlin,
2018) are relevant and non-trivial subjects in criminal investigations and law enforcement, since empirical evidence has shown that the dismantling process might potentially make these criminal organizations stronger (Duijn, Kashirin & Sloot,
2014). In addition, when it comes to fighting corruption the goal is clear: one not only is looking to describe it post factum, but to predict it (Rumi, Deng & Salim,
2018; Alves, Ribeiro & Rodrigues,
2018; López-Iturriaga & Sanz,
2018; Colonnelli et al.,
2019; Wachs et al.,
2019; Wachs & Kertész,
2019; Colliri & Zhao,
2019).
In summary, though corruption studies are diverse and tackle different aspects of the phenomenon, complex systems and network science approaches allow us to establish practical aspects for its investigation (Sayama,
2015; De Domenico et al.,
2019), mainly:
I.Components and interactions. Complex systems are usually comprised of large sets of interacting elements or components. Both the components and their interactions may be of different types.
II.Network structure. The structure of a complex system may be described as a network of interactions and interrelations in which all nodes and edges evolve as a whole over time.
III.Self-organization. There are many interactions among components. These occur independently, with no need of intervention by central organizing agents, producing collective non-trivial phenomena.
IV.Emergence. The collective behavior and properties of these systems can neither be predicted nor understood from the individual behavior or properties of each component in isolation.
V.Predictability and control. The dynamics, or temporal evolution, of a complex system are collective and often non-linear which, under certain conditions, makes the system highly unpredictable and difficult to control.
To show the usefulness of approaching the study of corruption through the complexity perspective, we will now analyze one of the most important corruption scandals in Mexico of the past decade.