Degree-targeted cascades in modular, degree-heterogeneous networks

Many large scale phenomena, such as rapid changes in public opinion and the outbreak of disease epidemics, can be fruitfully modeled as cascades of activation on networks. This provides under- standing of how various connectivity patterns among agents can influence the eventual extent of a cascade. We consider cascading dynamics on modular, degree-heterogeneous networks, as such features are observed in many real-world networks, and consider specifically the impact of the seeding strategy. We derive an analytic set of equations for the system by introducing a reduced description that extends a method developed by Gleeson that lets us accurately capture different seeding strategies using only one dynamical variable per module, namely the conditional exposure probability. We establish that activating the highest-degree nodes rather than random selection is more effective at growing a cascade locally, while the ability of a cascade to fully activate other modules is determined by the extent of large-scale interconnection between modules and is independent of how seed nodes are selected.