connected graphs

edit

Following the link given by @kcrisman you learn about nauty_geng.

sage: gen = graphs.nauty_geng("9 -c")
sage: sum(1 for g in gen)
261080

You may find this link helpful. Though perhaps connectedness isn't heritable, so be warned:

Remember that the property argument does not behave as a filter, except for appropriately inheritable properties:

Still, on that page you should find a syntax that helps you.