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We discuss some social contagion processes to describe the formation and spread of radical opinions. The dynamics of opinion spread involves local threshold processes as well as mean field effects. We calculate and observe phase transitions in the dynamical variables resulting in a rapidly increasing number of passive supporters. This strongly indicates that military solutions are inappropriate.
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The rapid spread of radical ideologies has led to a world-wide succession of terrorist attacks in recent years. Understanding how extremist tendencies germinate, develop, and drive individuals to action is important from a cultural standpoint, but also to help formulate response and prevention strategies. Demographic studies, interviews with radicalized subjects, analysis of terrorist databases, reveal that the path to radicalization occurs along progressive steps, where age, social context and peer-to-peer exchanges play major roles. To execute terrorist attacks, radicals must efficiently communicate with one another while maintaining secrecy; they are also subject to pressure from counter-terrorism agencies, public opinion and the need for material resources. Similarly, government entities must gauge which intervention methods are most effective. While a complete understanding of the processes that lead to extremism and violence, and of which deterrents are optimal, is still lacking, mathematical modelers have contributed to the discourse by using tools from statistical mechanics and applied mathematics to describe existing and novel paradigms, and to propose novel counter-terrorism strategies. We review some of their approaches in this work, including compartment models for populations of increasingly extreme views, continuous time models for age-structured radical populations, radicalization as social contagion processes on lattices and social networks, agent based models, game theoretic formulations. We highlight the useful insights offered by analyzing radicalization and terrorism through quantitative frameworks. Finally, we discuss the role of institutional intervention and the stages at which de-radicalization strategies might be most effective.
We investigate the effect of clustering on network observability transitions. In the observability model introduced by Yang, Wang, and Motter [Phys. Rev. Lett. 109, 258701 (2012)], a given fraction of nodes are chosen randomly, and they and those neighbors are considered to be observable, while the other nodes are unobservable. For the observability model on random clustered networks, we derive the normalized sizes of the largest observable component (LOC) and largest unobservable component (LUC). Considering the case where the numbers of edges and triangles of each node are given by the Poisson distribution, we find that both LOC and LUC are affected by the networks clustering: more highly-clustered networks have lower critical node fractions for forming macroscopic LOC and LUC, but this effect is small, becoming almost negligible unless the average degree is small. We also evaluate bounds for these critical points to confirm clusterings weak or negligible effect on the network observability transition. The accuracy of our analytical treatment is confirmed by Monte Carlo simulations.
Hypergraphs naturally represent higher-order interactions, which persistently appear from social interactions to neural networks and other natural systems. Although their importance is well recognized, a theoretical framework to describe general dynamical processes on hypergraphs is not available yet. In this paper, we bridge this gap and derive expressions for the stability of dynamical systems defined on an arbitrary hypergraph. The framework allows us to reveal that, near the fixed point, the relevant structure is the graph-projection of the hypergraph and that it is possible to identify the role of each structural order for a given process. We also analytically solve two dynamics of general interest, namely, social contagion and diffusion processes, and show that the stability conditions can be decoupled in structural and dynamical components. Our results show that in social contagion processes, only pairwise interactions play a role in the stability of the absorbing state, while for the diffusion dynamics, the order of the interactions plays a differential role. Ours is the first attempt to provide a general framework for further exploration of dynamical processes on hypergraphs.
In social networks, the collective behavior of large populations can be shaped by a small set of influencers through a cascading process induced by peer pressure. For large-scale networks, efficient identification of multiple influential spreaders with a linear algorithm in threshold models that exhibit a first-order transition still remains a challenging task. Here we address this issue by exploring the collective influence in general threshold models of behavior cascading. Our analysis reveals that the importance of spreaders is fixed by the subcritical paths along which cascades propagate: the number of subcritical paths attached to each spreader determines its contribution to global cascades. The concept of subcritical path allows us to introduce a linearly scalable algorithm for massively large-scale networks. Results in both synthetic random graphs and real networks show that the proposed method can achieve larger collective influence given same number of seeds compared with other linearly scalable heuristic approaches.
It is widely believed that information spread on social media is a percolation process, with parallels to phase transitions in theoretical physics. However, evidence for this hypothesis is limited, as phase transitions have not been directly observed in any social media. Here, through analysis of 100 million Weibo and 40 million Twitter users, we identify percolation-like spread, and find that it happens more readily than current theoretical models would predict. The lower percolation threshold can be explained by the existence of positive feedback in the coevolution between network structure and user activity level, such that more active users gain more followers. Moreover, this coevolution induces an extreme imbalance in users influence. Our findings indicate that the ability of information to spread across social networks is higher than expected, with implications for many information spread problems.
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