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According to the documentation, GraphQuery is for interfacing with a database that has graphs up to 7 vertices but your question wants graphs on 9 vertices. When I wrote code similar to below using GraphQuery rather than list(graphs( the code stopped working at 8 vertices. The following code should work in a notebook:

M = []
L = list(graphs(9))
for i in range(0,len(L)):
    if not L[i].is_long_hole_free() and L[i].is_connected():
        M += [L[i]]
graphs_list.show_graphs(M)

I say should because I've had it running for over 2.5 hours and still no result. Of course, rendering thousands upon thousands of graphs will take a lot of time. On my quad core with 8 gigs of RAM, 8 vertices worked. But it took about 10 minutes and gobbled up over 90 percent of my RAM.

According to the documentation, GraphQuery is for interfacing with a database that has graphs up to 7 vertices but your question wants graphs on 9 vertices. When I wrote code similar to below using GraphQuery rather than list(graphs( the code stopped working at 8 vertices. The following code should work in a notebook:

M = []
L = list(graphs(9))
for i in range(0,len(L)):
    if not L[i].is_long_hole_free() and L[i].is_connected():
        M += [L[i]]
graphs_list.show_graphs(M)

I say should because I've had it running for over 2.5 hours and still no result. Of course, rendering thousands upon thousands of graphs will take a lot of time. On my quad core with 8 gigs of RAM, 8 vertices worked. But it took about 10 minutes and gobbled up over 90 percent of my RAM.RAM. EDIT: Still no result after 5 hours so I stopped it.