# Interactive Levy Flight in Interest Space

## TL;DR

This paper models online user interests as a Levy Flight in a virtual interest space, incorporating user interactions via digital resources, and successfully reproduces observed scaling laws in online attention networks.

## Contribution

It introduces a novel Levy Flight model for interest dynamics in virtual space that accounts for user interactions and matches empirical scaling laws.

## Key findings

- The model reproduces scaling laws of real online attention networks.
- Parameters inferred from the model describe individual user behaviors.
- The approach offers insights into online human behaviors and potential applications.

## Abstract

Compared to the well-studied topic of human mobility in real geographic space, very few studies focus on human mobility in virtual space, such as interests, knowledge, ideas, and so forth. However, it relates to the issues of management of public opinions, knowledge diffusion, and innovation. In this paper, we assume that the interests of a group of online users can span a Euclidean space which is called interest space, and the transfers of user interests can be modeled as the Levy Flight on the interest space. To consider the interaction between users, we assume that the random walkers are not independent but interact each other indirectly via the digital resources in the interest space. The model can successfully reproduce a set of scaling laws for describing the growth of the attention flow networks of real online communities, and the ranges of the exponents of the scaling are similar with the empirical data. Further, we can infer parameters for describing the individual behaviors of the users according to the scaling laws of the empirical attention flow network. Our model can not only provide theoretical understanding on human online behaviors, but also has wide potential applications, such as dissemination and management of public opinions, online recommendation, etc.