Diffusion approximation of a network model of meme popularity

TL;DR

This paper develops a diffusion approximation model for meme popularity on social networks, capturing individual meme dynamics and enabling efficient simulation and analysis of their trajectories.

Contribution

It introduces a novel stochastic process framework for modeling meme propagation, incorporating stable distribution theory to describe individual meme trajectories.

Findings

Successfully models heavy-tailed popularity distributions

Decouples meme trajectories for parallel simulation

Expresses dynamics through Fokker-Planck equations

Abstract

Models of meme propagation on social networks, in which memes compete for limited user attention, can successfully reproduce the heavy-tailed popularity distributions observed in online settings. While system-wide popularity distributions have been derived analytically, the dynamics of individual meme trajectories have thus far evaded description. To address this, we formulate the diffusion of a given meme as a one-dimensional stochastic process, whose fluctuations result from aggregating local network dynamics using classic and generalised central limit theorems, with the latter based on stable distribution theory. Ultimately, our approach decouples competing trajectories of meme popularities, allowing them to be simulated independently, and thus parallelised, and expressed in terms of Fokker-Planck equations.