Influence of Affinity and Proximity on Consensus Formation in Social Networks}

Scale-free networks often optimize adaptability, information flow, and robustness, being present in several complex systems, from protein interactions to neural connections to the internet, power grids, and food webs. However, traditional scale-free models fail to predict the affinity-based and spatial patterns present in social networks. In this work, we investigate the effects of affinity and proximity on social networks with social attraction, better representing real-world social network structures. We also explore these network features on group social dynamics using the majority-vote model -- a straightforward framework for illustrating opinion evolution in elections, debates, and financial markets. In this model, each individual can hold one of two opinions on a given subject and time, favor or against it, influenced by their social connections. A noise parameter q introduces a social nonconformism, enabling a behavioral social disorder. With probability (1-q), agents tend to conform to the prevailing opinion within their social interaction network, while with chance q, they act in nonconformity. We perform Monte Carlo simulations to evaluate the social consensus and critical behavior to uncover how affinity and proximity affect network structure and social dynamics.