Giant Cluster Emergence and Functionality in Social Systems

The emergence of a giant cluster, in which bits and pieces of otherwise unconnected parts of a system come together, has been extensively studied in nonsocial contexts. This phenomenon has attracted substantial attention because it allows researchers to understand and predict the collective behavior of a system. In this paper, we formalize the emergence and functionality of a giant cluster within a social system. It has been well established that giant clusters can easily emerge in systems with few triads and abundant bridges. However, studies have shown that social networks are characterized by abundant triads and a limited number of bridges. This finding implies that people are more likely to interact with others and form ties within a common shared context. The finding also suggests that it is costly for people to cross the boundaries of their own social circle and to build bridges connecting to the outside world. A question is whether a giant cluster can also emerge even under these seemingly unfavorable conditions. In our paper, we develop simple models to address this question. Our models reveal that even if bridges constitute only a tiny fraction of the ties in a system, a giant cluster can emerge. Furthermore, we find that giant clusters in systems with a limited number of bridges are more conducive to innovation than giant clusters with abundant bridges, which tend to stifle knowledge creation.