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arXiv · 2503.18444

Dominant Groups and Asymmetric Polarization in Generalized Quasi-Structurally Balanced Networks

Vishnudatta Thota·Swati Priya·Twinkle Tripathy
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Abstract

The paper focuses on the phenomenon of asymmetric polarization arising in the presence of a dominant group in the network. The existing works in the literature analyze polarization primarily in structurally and quasi-structurally balanced networks. In this work, we introduce generalized quasi-structurally balanced (GQSB) networks, which include both of these networks as special cases. In the presence of a dominant group, a GQSB network has a unique bipartition: the dominant group (and its allies) and the remaining agents. The dominant group's superior influence results in an asymmetry in how the inter-subset antagonistic interactions are perceived by both of the subsets. This, in turn, leads to asymmetry in the final polarized opinions. To model this behavior, we propose a generalized Laplacian flow for undirected GQSB networks with a dominant group and establish necessary and sufficient conditions for achieving asymmetric polarization. The theoretical results presented in this paper are validated through numerical simulations on the Highland Tribes real-world dataset.

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Vishnudatta Thota, Swati Priya, Twinkle Tripathy. 2025-03-24. Dominant Groups and Asymmetric Polarization in Generalized Quasi-Structurally Balanced Networks. https://arxiv.org/abs/2503.18444

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