Abstarct: Since network break up and classification is one of social network analysis goals. Network classification is the key to understand large and complex network. Therefore in this dissertation is studying network analysis subject with equivalence method. In classification problem, is understanding individuals position and similarity measure. In first chapter of dissertation, introduce preliminary concepts that are requirement for next chapters. In chapter 2, are studied history of social networks and social network analysis and also classification of individuals with use structure equivalence method. In chapter 3, use other classification method that is called regular equivalence. In chapter 4, introduce a sequence for computing greatest regular equivalence with residulas and relation composed. In chapter 5, introduce fuzzy social networks and is studying exist greatest fuzzy and crisp equivalence in this networks and research a sequence for greatest with all cases of truth values sets in the fuzzy logic that are called complete residuated complete. In chapter 6, introduce weak and strong fuzzy regular.