Clarification regarding Q4: Q4 mentions "We add a new central node B to the network, and connect it with every other node on the ring...". Note that the "every other node" should just read as "every node" on the ring. It does NOT mean alternate nodes. So every node on the ring is linked to B independently with probability p.
If anyone has already done with the other meaning, you do not need to redo it. Sorry for the confusion!
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