It is well discussed in many graph theory texts that it is somewhat hard to distinguish non-isomorphic graphs with large order. But as to the construction of all the non-isomorphic graphs of any given order not as much is said. So, it follows logically to look for an algorithm or method that finds all these graphs.

A Google search shows that a paper by P. O. de Wet gives a simple construction that yields approximately $\sqrt{T_n}$ non-isomorphic graphs of order n.

( $\{T_n}$ being the number of labeled graphs of order n.)

So, I have the followings to ponder over:

(1) Are there such algorithms or has there been an improvement on the aforementioned algorithm?

(2) Where can I find a collection of non-isomorphic graphs of a given order?

If you allow me, I would also like to extend my question to connected graphs.

Many thanks.

(I am a beginner in Graph theory, so please give answers in not-very-specialized terms.)