Impact of Community Structure on Cascades

Abstract

The threshold model is widely used to study the propagation of opinions and technologies in social networks. In this model individuals adopt the new behavior based on how many neighbors have already chosen it. We study cascades under the threshold model on sparse random graphs with community structure to see whether the existence of communities affects the number of individuals who finally adopt the new behavior. Specifically, we consider the permanent adoption model where nodes that have adopted the new behavior cannot change their state. When seeding a small number of agents with the new behavior, the community structure has little effect on the final proportion of people that adopt it, i.e., the contagion threshold is the same as if there were just one community. On the other hand, seeding a fraction of population with the new behavior has a significant impact on the cascade with the optimal seeding strategy depending on how strongly the communities are connected. In particular, when the communities are strongly connected, seeding in one community outperforms the symmetric seeding strategy that seeds equally in all communities.

Cascading Failures in Interdependent Systems: Impact of Degree Variability and Dependence

“…There are many other important properties, such as assortativity [34], [35] and clustering [11], [46] often observed in social networks or engineered systems as well as community structure [29], which influence the dynamics of information or failure propagation. But, as it will be clear, even without these properties, analyzing the role of degree variability and dependence is technically challenging.…”

“…Given the significant body of studies in related fields, it is not possible to provide a summary of all. For this reason, we limit our discussion to a short list of most pertinent studies in the settings of multiplex or interdependent networks, and do not discuss other relevant studies (e.g., [2], [6], [14], [26], [29], [42]), including many important studies on a single, monolithic network (e.g., [3], [8], [9], [11], [22], [30], [31], [34], [35], [44]), here. We instead refer an interested reader to the references and those therein.…”

Analysis and Interventions in Large Network Games

“…In a simple contagion model, random seeding is therefore sufficient for central agents to be infected at a later iteration. The assumption of simple contagion is crucial for the discussion above, complex contagion models (where a fraction of the neighbors needs to be active for contagion to propagate) require careful placement of the initial seeds even for large populations, see e.g., Jackson and Storms (2019); Moharrami et al (2016); Erol et al (2020).…”

“…Extensions of the results above to generalizations of the configuration model have been discussed for example in Amini et al (2016), which considers weighted directed networks in the context of cascading failures in financial networks, or in Moharrami et al (2016), which focuses on the impact of community structure on the cascade dynamics by considering the weak interconnection of multiple graphs with bounded average degree generated from the configuration model. The paper Sadler (2020) considers diffusion games over standard and multi-type configuration models.…”

Influence of Clustering on Cascading Failures in Interdependent Systems

“…There is already extensive literature on the topic of epidemics, information propagation and cascading failures (e.g., [1], [3], [4], [7], [34], [44]), which cuts across multiple disciplines (e.g., epidemiology [11], [18], [37], [39], finance [8], [9], social networks [22], [33], and technological networks [12], [13], [27]). Given the large volume of literature, it would be an unwise exercise to attempt to provide a summary of all related studies.…”