The Impact of Heterogeneous Thresholds on Social Contagion with Multiple Initiators

TL;DR

This study explores how varying thresholds and multiple initiators affect social contagion, revealing non-monotonic cascade sizes, optimal opinion spread conditions, and size-independent spreading in complex networks.

Contribution

It introduces a detailed analysis of threshold heterogeneity and initiator effects on social contagion, highlighting non-monotonic behaviors and conditions for optimal spreading.

Findings

Cascade size varies non-monotonically with threshold distribution variance.

A large threshold spread eliminates tipping-point behavior, leading to smooth opinion spread.

Adding a single node to the initiator set can trigger global cascades.

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.