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For a given number of nodes how many non-isomorphic graphs are available? Might be this is an open problem. For less number of vertices some computational statistics available.

I want to get all non-isomorphic graphs of order $5, 6, \dots 12$. Is there any complete list of all non isomorphic graphs available for a given number of nodes? If possible please give me its links or some references.

If I wish to calculate it myself, which software package may be useful?

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Use Brendan McKay's program geng, which is distributed with the nauty/Traces package and is available from http://pallini.di.uniroma1.it/.

There are about 165091172592 graphs on 12 vertices, so it might take you a while.

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    $\begingroup$ one can also use nauty through sage $\endgroup$ – Kimball Jul 1 '15 at 10:39

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