Influence of relationship strengths to network structures in social network

Social network provide detailed records of human communication patterns, offering convenient way to information spreading and explore the structure of social networks. Here we provide a model to examine the relationship strengths of social network users, allowing us to simultaneously study diffident structure of social network. We observe a coupling between users' relationship strengths and network's structure, with the consequence that in some kind of social network the structure fall apart following a phase transition if the weak ties are removed, but in another kind of social network the structure is robust. We find that in the information exchanged social networks, removing the weak ties have little influence on the information spreading, while in the relationship of social network, removing the weak ties have significant influence on the information spreading.