Independence of the Fundamental Equation of the Oscillation Model on Algebraic Representations: Social Media Echo Chamber Effect

TL;DR

This paper demonstrates that the fundamental equation of the oscillation model for social media user dynamics yields consistent results regardless of the algebraic matrix representation used, confirmed through the echo chamber effect example.

Contribution

It proves the algebraic representation independence of the fundamental oscillation equation in social network models, ensuring consistent results across different matrix forms.

Findings

Different matrix representations produce the same results.

The fundamental equation's outcomes are invariant to algebraic form.

Confirmed the algebraic independence using the echo chamber effect.

Abstract

In the oscillation model that describes the user dynamics of online social networks, it is known that the fundamental equation can explicitly describe the causal relationship between the network structure and user dynamics. The fundamental equation uses algebra that satisfies the anti-commutation relation, and its matrix representation is not unique. However, even if the matrix representations are different, the same results should be derived from different representations of the fundamental equation if they are describing the same phenomenon. In this paper, we confirm, using the echo-chamber effect as an example, that the fundamental equations of different matrix representations lead to the same result.