I had a hard time imagining the former in the unit circle, but switching to y=x^2 was illustrative for me.
The transition between the complete connected graph on countably infinite nodes and uncountably many K_ב_0 and K_ב_1 is weird. Think about their embeddings in the unit circle.
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It's the limit of the complete graphs in this: https://math.stackexchange.com/questions/1129911/determine-the-number-of-paths-of-length-2-in-a-complete-graph-of-n-nodes …
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