Abstract
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 spread 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.
Highlights
The technological breakthroughs of the 21st century have strongly contributed to the emergence of network science, a multidisciplinary science with applications in many scientific fields and technologies
We studied the impact of diversity of thresholds in spreading a new opinion, by intuitively assuming that the adoption thresholds are drawn from a truncated normal distribution
We explored this impact by using the threshold model, a reinforcement model which has lately drawn significant attention in the doi:10.1371/journal.pone.0143020.g009
Summary
The technological breakthroughs of the 21st century have strongly contributed to the emergence of network science, a multidisciplinary science with applications in many scientific fields and technologies. Several sociological opinion diffusion models first introduced in the middle of 20th century are being thoroughly studied, while variations of these classical models have been introduced. Most of these models are based on social reinforcement, where simple rules based on the interaction of individuals with their respective nearest neighbors govern individual opinion evolution. The macroscopic outcome of these rules is a cascade of nodes switching opinions [1,2,3,4,5,6,7,8,9]. Under the TM a node adopts a new opinion only when the fraction of its nearest neighbors possessing that
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