The Impact of Heterogeneous Thresholds on Social Contagion with Multiple Initiators
by
Professor Gyorgy Korniss Department of Physics, Applied Physics, and Astronomy Rensselaer Polytechnic Institute
The threshold model is a simple but classic model of contagion spreading in complex social systems. To capture the complex nature of social influencing we investigate numerically and analytically the transition in the behavior of threshold-limited cascades in the presence of multiple initiators as the distribution of thresholds is varied between the two extreme cases of identical thresholds and a uniform distribution. We accomplish this by employing a truncated normal distribution of the nodes’ thresholds and observe a non-monotonic change in the cascade size as we vary the standard deviation. Further, for a sufficiently large spread in the threshold distribution, the tipping-point behavior of the social influencing process disappears and is replaced by a smooth crossover governed by the size of initiator set. We demonstrate that for a given size of the initiator set, there is a specific variance of the threshold distribution for which an opinion spreads optimally. Furthermore, in the case of synthetic graphs we show that the fraction of active nodes asymptotically becomes independent of the system size, and that global cascades can arise just by the addition of a single node to the initiator set.
P.D. Karampourniotis, S. Sreenivasan, B.K. Szymanski, and G. Korniss, “The Impact of Heterogeneous Thresholds on Social Contagion with Multiple Initiators”, PLoS ONE 10(11): e0143020 (2015); http://dx.doi.org/10.1371/journal.pone.0143020.