In our recent work we found interesting and unintuitive patterns for time evolving networks, which change some of the basic assumptions that were made in the past. The main objective of observing the evolution patterns is to develop models that explain processes which govern the network evolution. Such models can then be fitted to real networks, and used to generate realistic graphs or give formal explanations about their properties. In addition, our work has a wide range of applications: we can spot anomalous graphs and outliers, design better graph sampling algorithms, forecast future graph structure and run simulations of network evolution. Another important aspect of this research is the study of "local" patterns and structures of propagation in networks. We aim to identify building blocks of the networks and find the patterns of influence that these block have on information or virus propagation over the network. Our recent work included the study of the spread of influence in a large person-to-person product recommendation network and its effect on purchases. We also model the propagation of information on the blogosphere, and propose algorithms to efficiently find influential nodes in the network. Further work will include three areas of research. We will continue investigating models for graph generation and evolution. Second, we will analyze large online communication networks and devise models on how user characteristics and geography relate to communication and network patterns. Third, we will extend the work on the propagation of influence in recommendation networks to blogs on the Web, studying how information spreads over the Web by finding influential blogs and analyzing their patterns of influence. ; : http://www.cs.cmu.edu/~jure/thesis/ ; Thesis Committee: : Christos Faloutsos (Chair) : Avrim Blum : John Kleinberg (Cornell University) : John Lafferty