Modeling the popularity of twitter hashtags with master equations

Area of Science:

• Computational Social Science
• Network Science
• Mathematical Modeling

Background:

• Understanding the dynamics of information spread on social media platforms like Twitter is crucial.
• Hashtag popularity is a key indicator of trending topics and user engagement.
• Existing models often lack a comprehensive approach to the temporal evolution of hashtag visibility.

Purpose of the Study:

• To introduce a novel mathematical model for describing the time evolution of hashtag popularity on Twitter.
• To provide explicit solutions for the mean and variance of hashtag appearance counts.
• To validate the model's efficacy using real-world Twitter data.

Main Methods:

• Development of a mathematical model based on master equations.
• Incorporation of internal network factors (e.g., degree distribution) and external factors (e.g., external popularity).
• Proposal of a gamma kernel function for modeling hashtag popularity.
• Validation against empirical data from the Twitter public API.

Main Results:

• The model successfully predicts the time evolution of hashtag popularity.
• Explicit solutions for mean and variance were derived, enabling confidence region construction.
• The gamma kernel function provided reasonable and accurate results.
• Model validation confirmed its ability to capture essential dynamics of hashtag spread.

Conclusions:

• Simple semi-deterministic models can effectively represent complex social network phenomena like hashtag popularity.
• The proposed model offers a unique focus on the temporal aspect and integrates both internal and external drivers of hashtag visibility.
• This work provides a valuable tool for analyzing and understanding information diffusion on Twitter.