Opinion Formation in Wikipedia Ising Networks

We study the properties of opinion formation on Wikipedia Ising Networks. Each Wikipedia article is represented as a node, and links are formed by citations of one article to another, generating a directed network of a given language edition with millions of nodes. Ising spins are placed at each node, and their orientation up or down is determined by a majority vote of connected neighbors. At the initial stage, there are only a few nodes from two groups with fixed competing opinions up and down, while other nodes are assumed to have no initial opinion with no effect on the vote. The competition of two opinions is modeled by an asynchronous Monte Carlo process converging to a spin-polarized steady-state phase. This phase remains stable with respect to small fluctuations induced by an effective temperature of the Monte Carlo process. The opinion polarization at the steady state provides opinion (spin) preferences for each node. In the framework of this Ising Network Opinion Formation model, we analyze the influence and competition between political leaders, world countries, and social concepts. This approach is also generalized to the competition between three groups of different opinions described by three colors; for example, Donald Trump, Vladimir Putin, and Xi Jinping, or the USA, Russia, and China, within English, Russian, and Chinese editions of Wikipedia of March 2025. We argue that this approach provides a generic description of opinion formation in various complex networks.