PageRank model of opinion formation on Ulam networks

TL;DR

This paper models opinion formation on Ulam networks generated by specific maps, revealing similarities and differences with scale-free networks like the WWW, and analyzes opinion dynamics using a generalized Sznajd model.

Contribution

It introduces a PageRank-based opinion formation model on Ulam networks and compares its features with those of scale-free networks such as the WWW.

Findings

Ulam networks exhibit algebraic decay of PageRank similar to WWW.

Opinion formation dynamics show both similarities and differences with WWW networks.

The generalized Sznajd model highlights the protection of small community opinions.

Abstract

We consider a PageRank model of opinion formation on Ulam networks, generated by the intermittency map and the typical Chirikov map. The Ulam networks generated by these maps have certain similarities with such scale-free networks as the World Wide Web (WWW), showing an algebraic decay of the PageRank probability. We find that the opinion formation process on Ulam networks have certain similarities but also distinct features comparing to the WWW. We attribute these distinctions to internal differences in network structure of the Ulam and WWW networks. We also analyze the process of opinion formation in the frame of generalized Sznajd model which protects opinion of small communities.