Threshold-limited spreading in social networks with multiple initiators

TL;DR

This paper investigates how multiple initiators trigger opinion cascades in social networks with uniform thresholds, highlighting the role of network structure and initiator strategies in enabling large-scale influence spread.

Contribution

It introduces a comprehensive analysis of threshold-driven cascades with multiple initiators, emphasizing the impact of network clustering and community structure on cascade size.

Findings

Existence of a critical initiator fraction for global cascades at any threshold.

Community structure enhances opinion spread compared to random networks.

Different initiator selection strategies significantly affect cascade outcomes.

Abstract

A classical model for social-influence-driven opinion change is the threshold model. Here we study cascades of opinion change driven by threshold model dynamics in the case where multiple {\it initiators} trigger the cascade, and where all nodes possess the same adoption threshold $\phi$. Specifically, using empirical and stylized models of social networks, we study cascade size as a function of the initiator fraction $p$. We find that even for arbitrarily high value of $\phi$, there exists a critical initiator fraction $p_c(\phi)$ beyond which the cascade becomes global. Network structure, in particular clustering, plays a significant role in this scenario. Similarly to the case of single-node or single-clique initiators studied previously, we observe that community structure within the network facilitates opinion spread to a larger extent than a homogeneous random network. Finally, we study the efficacy of different initiator selection strategies on the size of the cascade and the cascade window.