Cascading behavior of an extended Watts model on networks

TL;DR

This paper extends the Watts model to include the influence of initiators with lower thresholds, analyzing how their presence affects the likelihood and size of information cascades in random networks.

Contribution

It introduces an extended Watts model with a tree approximation and derives cascade conditions considering initiator influence in random networks.

Findings

Increasing initiator influence promotes global cascades.

Fraction of initiators and node thresholds critically affect cascade dynamics.

Early-stage cascade behavior is determined by initiator connections.

Abstract

In this study, we propose an extended Watts model to examine the effect of initiators on information cascades. The extended Watts model assumes that nodes with connections to initiators have low adoption thresholds than other nodes, due to the significant influence of initiators. We develop a tree approximation to describe the active node fraction for the extended Watts model in random networks and derive the cascade condition for a global cascade to occur with a small fraction of initiators. By analyzing the active node fraction and the cascade window of the extended Watts model on the Erdos-Renyi random graph, we find that increasing the influence of initiators facilitates the possibility of global cascades, i.e., how many nodes eventually become active is significantly affected by the fraction of initiators and the threshold of nodes directly connected to initiators, which determine cascade dynamics at early stages.