Connections between the Sznajd Model with General Confidence Rules and graph theory

Abstract

The Sznajd model is a sociophysics model, that is used to model opinion propagation and consensus formation in societies. Its main feature is that its rules favour bigger groups of agreeing people. In a previous work, we generalized the bounded confidence rule in order to model biases and prejudices in discrete opinion models. In that work, we applied this modification to the Sznajd model and presented some preliminary results. The present work extends what we did in that paper. We present results linking many of the properties of the mean-field fixed points, with only a few qualitative aspects of the confidence rule (the biases and prejudices modelled), finding an interesting connection with graph theory problems. More precisely, we link the existence of fixed points with the notion of strongly connected graphs and the stability of fixed points with the problem of finding the maximal independent sets of a graph. We present some graph theory concepts, together with examples, and comparisons between the mean-field and simulations in Barabási-Albert networks, followed by the main mathematical ideas and appendices with the rigorous proofs of our claims. We also show that there is no qualitative difference in the mean-field results if we require that a group of size q>2, instead of a pair, of agreeing agents be formed before they attempt to convince other sites (for the mean-field, this would coincide with the q-voter model).

15 pages, 18 figures. To be submitted to Physical Review

References in corpus (5)

• Statistical physics of social dynamics
• Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games
• Phase transition in the Sznajd model with independence
• Exit probability in a one-dimensional nonlinear q-voter model
• Coexistence of Interacting Opinions in a Generalized Sznajd Model

Cited by in corpus (4)

• Opinion dynamics: models, extensions and external effects
• Statistical Physics Of Opinion Formation: is it a SPOOF?
• On the exit probability of the one dimensional q-voter model. Analytical results and simulations for large networks
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