Emergence of the web and online computing applications gave rich data on human social activity that can be represented in a form of an interaction graph. One of the principal challenges then is to build models and understanding of the structure of such large networks. In this talk I will present our work on the cluster or community structure in large networks, where clusters are thought of as sets of nodes that are better connected internally than to the rest of the network. We find that large networks have very different clustering structure from well studied small social networks and graphs that are well-embeddable in a low-dimensional structure. In networks of millions of nodes tight clusters exist at only very small size scales up to around 100 nodes, while at large size scales networks becomes expander like. As this behavior is not explained, even at a qualitative level, by any of the commonly-used network generation models I will then present a network model based on Kronecker products that is able to produce graphs exhibiting a network structure similar to our observations.