Modeling trend progression through an extension of the Polya Urn Process

TL;DR

This paper models the progression of social trends using an extended Polya Urn process, revealing power-law behavior in trend spread through networks, supported by theoretical analysis and simulations.

Contribution

It introduces a novel extension of the Polya Urn process to model trend progression in social networks, linking it to a random graph model.

Findings

Component size distribution follows a power-law.

Model maps RG states to Polya process states.

Simulations support theoretical results.

Abstract

Knowing how and when trends are formed is a frequently visited research goal. In our work, we focus on the progression of trends through (social) networks. We use a random graph (RG) model to mimic the progression of a trend through the network. The context of the trend is not included in our model. We show that every state of the RG model maps to a state of the Polya process. We find that the limit of the component size distribution of the RG model shows power-law behaviour. These results are also supported by simulations.