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

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