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Figured it out myself.

My iteration starts with a graph of just one edge, then adds different types of edges to it. Initially, I had

G=Graph({0:[1],1:[]})

I checked in detail through the Sage manual pages on graphs, and found that there are options multiedges and loops that can be set for a given graph. So now I have

G=Graph(multiedges=True,loops=True)
G.add_edge(0,1)

This gives me exactly what I want. Now G.add_edge(0,0) adds a loop to the graph, and G.add_edge(0,1) makes it have a pair of multiple edges.

My problem was that Sage assumes False values by default for these options, meaning that a graph by default is simple.