Modelling meme popularity with networks

Abstract

Memes are pieces of information transmitted from person to person. In online social media platforms, the measurement of memes reveals intricate patterns that emerge from the underlying social network formed from interacting users. Most of the memes are not transmitted many times, but a few become extremely popular. In this thesis,we study the meme popularity phenomena with mathematical and computational methods. Our contribution is divided in two parts, as follows.

First, we consider a meme-copying mechanism called the competition-induced criticality model. In this model, meme popularity evolves in discrete jumps from individual transmission events. We reformu-late this model by approximating this jump process with a diffusion process. In so doing, we reproduce meme popularity distributions similarly to the original model, via stochastic differential equations.

The diffusion approximation relies on the central limit theorem, as well as its extension, the generalised central limit theorem. Further-more, the approximation also allows for novel analytical characterisation of the system by highlighting the effect of degree heterogeneity, further shedding light on how the diffusion approximation works.

Second, we propose a framework to extend models so that users may discriminate memes as they are copied. It tests different hypotheses of how memes are copied, for which we rely on a dataset of Twitter hashtags representing memes. Of the four hypotheses we tested, the one closest to the dataset measurements is based on topical alignment,or the propensity of users to interact with others who communicate about the same topics.