This paper proposes a set of criteria that permit to establish the Quality of Social Network (QoSN) of a social network that consists of social Web services. These latter are quite different from (regular) Web services since they can, among other things, establish and maintain networks of contacts, count on their contacts when needed, and form with other peers strong and long lasting collaborative groups. A social Web service can sign up in three types of social networks referred to as competition, collaboration, and substitution. Prior to signing up the social Web service checks the privacy, trust, fairness, and traceability criteria that constitute the social network’s QoSN. The interpretation and evaluation of each criterion vary from one social network to another.