On the fundamental equation of user dynamics and the structure of online social networks

Online social networks suffer from explosive user dynamics such as flaming that can seriously affect social activities in the real world because the dynamics have growth rates that can overwhelm our rational decision making faculties. Therefore, a deeper understanding of user dynamics in online social networks is a fundamental problem in computer and information science. One of the effective user dynamics models is the networked oscillation model; it uses a second-order differential equation with Laplacian matrix. Although our previous study indicates that the oscillation model provides us with a minimal but effective model of user interactions, there still remains the open problem as to the existence of a first-order fundamental differential equation that respects the structure of the original network. This paper fills in this gap and shows that, by doubling the dimension of the state space, we can explicitly but naturally construct a fundamental equation that fully respects the structure of the original network.Comment: 7 pages, 2 figures. This is a typo-fixed version of the paper published in NetSci-X 202

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

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.Comment: 4 pages, no figure, IEICE ICETC 2020. arXiv admin note: substantial text overlap with arXiv:2011.1337

Closed-Form Solutions of the Fundamental Equation That Describes User Dynamics in Online Social Networks

The oscillation model, based on the wave equation on networks, can describe user dynamics in online social networks. The fundamental equation of user dynamics can be introduced into the oscillation model to explicitly describe the causal relation of user dynamics yielded by certain specific network structures. Moreover, by considering the sparseness of online social networks, a novel fundamental equation of different form has been devised. In this paper, we derive a closed-form solution of the new fundamental equation. Also, we find the closed-form solution of the new fundamental equation can generate the general solution of the original wave equation.Comment: 7 pages, 2 figures, CANDAR 2020 W

Polarization Model of Online Social Networks Based on the Concept of Spontaneous Symmetry Breaking

The spread of information networks has not only made it easier for people to access a variety of information sources but also greatly enhanced the ability of individuals to disseminate information. Unfortunately, however, the problem of slander in online social networks shows that the evolving information network environment does not necessarily support mutual understanding in society. Since information with particular bias is distributed only to those communities that prefer it, the division of society into various opposing groups is strengthened. This phenomenon is called polarization. It is necessary to understand the mechanism of polarization to establish technologies that can counter polarization. This paper introduces a fundamental model for understanding polarization that is based on the concept of spontaneous symmetry breaking; our starting point is the oscillation model that describes user dynamics in online social networks.Comment: 8 pages, 6 figures, the typo fixed version of ITC3

Derivation and Characteristics of Closed-Form Solutions of the Fundamental Equations for Online User Dynamics

The oscillation model, based on the wave equation on networks, can describe user dynamics in online social networks. The fundamental equation of user dynamics can be introduced into the oscillation model to explicitly describe the causal relation of user dynamics yielded by certain specific network structures. Moreover, by considering the sparseness of the link structure of online social networks, a novel fundamental equation of different forms has been devised. In this paper, we derive a closed-form solution of the new fundamental equation. Also, we show that the closed-form solution of the new fundamental equation can generate the general solution of the original wave equation and investigate the characteristics of the derived general solution.Comment: 16 pages, 8 figures. arXiv admin note: substantial text overlap with arXiv:2011.0539