Graphs have evolved into a rich framework for the solution of diverse problems, ranging from mathematical puzzles to the analysis of planetary-scale social networks. A particular class of problems that has attracted recent interest in the research community is related to how to model information that is embedded in a graph structure. In this scenario, the graph dynamics is guided by processes that are localized both in time and space, with effects at different scales. For instance, traffic in road networks and content popularity on the Web are two scenarios where understanding the role played by network processes (e.g. traffic jams, information diffusion) might lead to new models, algorithms, and data structures for managing large dynamic graphs. We are developing methods for modeling and analyzing network processes using ideas from graph theory, information theory, and sampling.