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If G is your Sage graph, you can turn it into a networkx graph with the networkx_graph as in the following example:
sage: from networkx import algebraic_connectivity as AlgebraicConnectivity
sage: G = graphs.PetersenGraph()
sage: H = G.networkx_graph()
sage: AlgebraicConnectivity(H)
1.9999999999999993
sage: G = graphs.CompleteGraph(12)
sage: H = G.networkx_graph()
sage: AlgebraicConnectivity(H)
11.999999999999998
