Single-Seed Cascades on Clustered Networks

TL;DR

This paper analyzes how a single seed initiates cascades in clustered networks using adapted branching process models, providing insights into cascade extinction probabilities and extending existing theoretical frameworks.

Contribution

It introduces a novel two-type branching process model for single-seed cascades on clustered networks, extending prior tree-based methods to account for clustering effects.

Findings

Derived a fixed-point equation for cascade extinction probability.

Reproduced and extended Hackett et al.'s formula for cascade extinction.

Provided a theoretical framework for understanding cascades from a single seed in clustered networks.

Abstract

We consider a dynamic network cascade process developed by Watts applied to a random networks with a specified amount of clustering, belonging to a class of random networks developed by Newman. We adapt existing tree-based methods to formulate an appropriate two-type branching process to describe the spread of a cascade started with a single active node, and obtain a fixed-point equation to implicitly express the extinction probability of such a cascade. In so doing, we also recover a special case of a formula of Hackett et al. giving conditions for certain extinction of the cascade.