Abstract— Group Key Agreement with the Local Connectivity. A group key agreement problem where a user is the only aware of his neighbors while the connectivity graph is arbitrary. In our problem, there is no centralized initialization for users. A group key agreement with these features is the very < Final Year Projects 2016 > suitable for a social networks. Under our setting, we construct two efficient protocols with passive security. We obtain lower bounds on the round complexity for this type of protocol, which demonstrates that our constructions are round efﬁcient. Finally, we construct an actively secure protocol from a passively secure one. A user is the only aware of his neighbors while the connectivity graph is arbitrary.