Electronic databases, from phone to emails logs, currently provide detailed records of human communication patterns, offering novel avenues to map and explore the structure of social and communication networks. We examine the communication patterns of millions of mobile phone users, allowing us to simultaneously study the local and the global structure of a society-wide communication network. We observe a coupling between interaction strengths and the networks local structure, and conclude that social networks are robust to the removal of the strong ties, but fall apart following a phase transition if the weak ties are removed. We show that this coupling significantly slows the diffusion process, resulting in dynamic trapping of information in communities, and find that when it comes to information diffusion, weak and strong ties are for different reasons both simultaneously ineffective. Using the aggregate records of a mobile phone service provider about private voice calls of more than 4 million users we construct over 18 weeks a weighted network of interactions where the tie strength is taken proportional to the total duration of the calls. We introduce a measure of the link overlap and show that nodes (i.e., people) with strong links have a large friendship overlap. This way we prove for the first time the Granovetter hypothesis about the strength of weak ties at a societal scale. The network has a strongly modular structure with highly wired communities with strong ties, which are connected by weak links. A global consequence of this structure is that the network connectedness is resilient against removal of strong links while it falls apart whenthe weak links are cancelled. The intimate relationship between link weights and topology has strong influence on the dynamic properties of the network. Using the simplest diffusive spreading dynamics we demonstrated that the probability of getting new information (or, alternatively, getting infected) via a strong or weak link is low, in most cases links with an intermediate strength play the role of the transmitter. In order to understand the peculiar interplay between topology and link weights we constructed a model of the social network. The model has strong simplifications and is based on elementary steps of link formation and tie strengthening. We deal with a constant number of nodes. In order to reach stationarity time to time a node is eliminated and, at the same time, a new one without any connections is born. Links are created either at random (with very low probability), or using already existing links (friends of friends get friends). An important element of the model is that whenever a link is used, there is a strengthening effect, described by a parameter σ. The resulting network describes well the qualitative features of the call network, including the strength of the weak ties and the trapping effect.