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Combine two graphs by merging a vertex

I need to draw a connected graph whose blocks are either complete graphs or cycles. Can I draw my graph by drawing the individual blocks first and then merging the appropriate vertices? For example if I need a connected graph with 10 vertives, where the first 5 vertices form a clique and the last 6 vertices form a cycle. I tried the following, but that didn't work.

g=graphs.CompleteGraph(5) h=graphs.CycleGraph(6) l=g.set_vertex(4, h)