Quantifying the Influence of Motif Decay on Information Diffusion in Online Social Networks via Structural Perturbation Models

Abstract

Characterizing how local topological motifs govern global cascades on temporal networks is crucial for predicting virality and designing interventions. While temporal motifs capture sequential interaction patterns, their functional role in driving or constraining dynamic spreading cascades remains less understood. To investigate this relationship, we present a null-model framework that systematically perturbs network structure to control motif decay. This allows us to quantify the relationship between SIR spreading dynamics and various temporal motif densities, including feed-forward loops (FFLs), shared neighbors, hubness, and edge recurrence, across undirected and directed networks. We demonstrate that subcritical transmission rates mask these correlations due to signal attenuation, whereas simulating diffusion above the epidemic threshold reveals high topology-diffusion correlations $(\vert\rho\vert$ up to $0.9945, p<0.001)$. Our analysis shows that edge recurrence consistently constrains spreading, as repeated interactions between the same users confine the spread. In contrast, network modularity determines the functional role of triadic closure. In diffuse networks, FFLs and shared neigh-bors act as traps that confine cascades (e.g., $\rho_{\text{FFL}} \leq-0.62$), whereas in modular networks they act as facilitators that help bridge communities (e.g., $\rho_{\text{FFL}} \geq+0.53$). Furthermore, modeling networks as directed rather than undirected shows that tracking the specific direction of interactions captures spreading dynamics more accurately than simply counting mutual neighbors. Finally, we analyze how the choice of time-slicing window affects spreading paths, offering guidelines for snapshot aggregation. These findings show that local temporal motifs are highly predictive of global cascades, with their functional role determined by network modularity.