Where on the internet I can find a database of graphs?

You might want to look at Donald Knuth's Stanford GraphBase: A Platform for Combinatorial Computing (1994, 2009) and the accompanying website.

See also The Stony Brook Algorithm Repository.

There's a nice collection of data on regular graphs at Markus Meringer's webpage.

Sage (http://www.sagemath.org/) provides access to a large collection of graphs, as well as tools for working with them.