Analysis of a threshold model of social contagion on degree-correlated networks

Peter Sheridan Dodds, Joshua L. Payne
2009 Physical Review E  
We analytically determine when a range of abstract social contagion models permit global spreading from a single seed on degree-correlated random networks. We deduce the expected size of the largest vulnerable component, a network's tinderbox-like critical mass, as well as the probability that infecting a randomly chosen individual seed will trigger global spreading. In the appropriate limits, our results naturally reduce to standard ones for models of disease spreading and to the condition for
more » ... o the condition for the existence of a giant component. Recent advances in the distributed, infinite seed case allow us to further determine the final size of global spreading events, when they occur. To provide support for our results, we derive exact expressions for key spreading quantities for a simple yet rich family of random networks with bimodal degree distributions.
doi:10.1103/physreve.79.066115 pmid:19658572 fatcat:xtd25rxckrdcvmejo5xpszikr4