A simple model of global cascades on random hypergraphs

TL;DR

This paper develops a hypergraph-based model to analyze information cascades driven by higher-order interactions, revealing how seed size and network structure influence cascade thresholds.

Contribution

It introduces a novel double-threshold hypergraph framework for understanding cascades, extending traditional models to include higher-order interactions and fractional seed effects.

Findings

Connectivity patterns affect cascade boundaries asymmetrically.

As seed size approaches zero, asymmetry diminishes.

The model advances understanding of complex systems with higher-order interactions.

Abstract

This study introduces a comprehensive framework that situates information cascades within the domain of higher-order interactions, utilizing a double-threshold hypergraph model. We propose that individuals (nodes) gain awareness of information through each communication channel (hyperedge) once the number of information adopters surpasses a threshold $\phi_m$. However, actual adoption of the information only occurs when the cumulative influence across all communication channels exceeds a second threshold, $\phi_k$. We analytically derive the cascade condition for both the case of a single seed node using percolation methods and the case of any seed size employing mean-field approximation. Our findings underscore that when considering the fractional seed size, $r_0 \in (0,1]$, the connectivity pattern of the random hypergraph, characterized by the hyperdegree, $k$, and cardinality, $m$, distributions, exerts an asymmetric impact on the global cascade boundary. This asymmetry manifests in the observed differences in the boundaries of the global cascade within the $(\phi_m, \langle m \rangle)$ and $(\phi_k, \langle k \rangle)$ planes. However, as $r_0 \to 0$, this asymmetric effect gradually diminishes. Overall, by elucidating the mechanisms driving information cascades within a broader context of higher-order interactions, our research contributes to theoretical advancements in complex systems theory.