In recent years, the use of fuzzy graph theory in social network analysis has become increasingly prevalent. The study of social networks has numerous practical applications in real life. This chapter aims to explore various aspects of fuzzy social networks, including connectivity and the control of actors within a network. An small introduction to quantum social networks is presented. This emerging area of study has the ability to transform our understanding of social networks and their dynamics. Additionally, the potential applications of fuzzy social networks in detecting sarcasm and in the healthcare sector will be discussed.