You can compute non-trivial statistics about the entire web-graph (roughly |V|=3B, |E|=100B)on a single high-end server these days. Speaking from personal experience, a machine with > 64 cores and 1TB of RAM can compute connectivity, MSTs, and partition this graph in minutes. Are there graphs out there (with the exception of Facebook and Google's private graphs) that are so large as to be intractable without resorting to external-memory/distributed computing?