What do graphs look like? How do they evolve over time? How does influence/news/viruses propagate, over time? We present a long list of static and temporal laws, and some recent observations on real graphs. We show that fractals and self-similarity can explain several of the observed patterns, and we conclude with cascade analysis and a surprising result on virus propagation and immunization.

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), nineteen “best paper” awards (including two “test of time” awards), and four teaching awards. He is an ACM Fellow, he has served as a member of the executive committee of SIGKDD; he has published over 200 refereed articles, 11 book chapters and one monograph. He holds six patents and he has given over 35 tutorials and over 15 invited distinguished lectures. His research interests include data mining for graphs and streams, fractals, database performance, and indexing for mutimedia and bio-informatics data.