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It is just like last year:

algebraic_connectivity = lambda g: sorted(g.laplacian_matrix().eigenvalues())[1]
G = max(graphs.nauty_geng("10 11:11 -c"), key=algebraic_connectivity)
G

Here I also used nauty to restrict the number of edges to 11, for efficiency.

Of course there could be more than one such graph. Indeed, using the code from the old answer, the output is:

There are 2 graphs of (maximal) algebraic connectivity 1