Large graph mining - Patterns, explanations, and cascade analysis

Summary form only given, as follows. 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.