Group-based rewiring rules of binary opinion competition dynamics

The dynamics of competing opinions on networks has attracted multi-disciplinary research. Most modelling approaches assume uniform or heterogeneous behaviour among all individuals, while the role of distinctive group behaviour is rarely addressed. Here, we consider competition occurring between two opinion groups with bound rewiring rules, i.e., opinion-preferred rewiring, degree-preferred rewiring and random rewiring. When two opinions share a balanced initial proportion, opinion-preferred rewiring is superior to the other rules under low rewiring rates, and coexistence occurs under high rewiring rates. For unbalanced proportions, the best response rule for the minority/majority is unfixed, and this depends on the initial proportion and rewiring frequency. Furthermore, we find evolution processes for all competing cases belong to two categories. Evolution Category I shows an obvious correlation between opinion proportions and the density of discordant edges (connecting nodes with different opinions), and these trends can be effectively described by numerical approximations. However, for Evolution Category II, no such correlation exists for individuals or linking pairs, and an analysis of local structures reveals the emergence of large numbers of open triads with the same opinions, denoting group prevalence. This work broadens the understanding of opinion competition and inspires exploring group strategies employed in social dynamic systems.