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What do graphs look like? How do they evolve over time? How do we handle a graph with a billion nodes? We present a comprehensive list of static and temporal laws, grounded in recent observations on real graphs. We then present tools for discovering anomalies and patterns in graphs. Finally, we present an overview of the PEGASUS system which is designed to handle billion-node graphs using Hadoop. About the speaker: Christos Faloutsos is a Professor at Carnegie Mellon University. He has received the Presidential Young Investigator Award by the National Science Foundation (1989), the Research Contributions Award in ICDM 2006, the SIGKDD Innovations Award (2010), seventeen "best paper'' awards, (including two "test of time'') and four teaching awards. He has served as a member of the executive committee of SIGKDD; he is an ACM Fellow; he has published over 200 refereed articles, 11 book chapters and one monograph. He holds five patents and he has given over 30 tutorials and over 10 invited distinguished lectures. His research interests include data mining for graphs and streams, fractals, database performance, and indexing for multimedia and bio-informatics data.