This paper proposes a set of criteria used to establish the uality of ocial etwork (o) of a social network connecting social Web services together. These latter are quite different from (regular) Web services since they can, for instance 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 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 o. The interpretation and evaluation of each criterion vary from one social network to another. © 2012 Springer-Verlag GmbH Berlin Heidelberg.