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On Wikipedia, I tried a number of times to find the item I needed, starting from a random page and clicking on various (non-random) hyperlinks. Every time I succeeded in finding my desired item. Is this always possible?

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    $\begingroup$ It is possible if and only if the graph has exactly one strongly connected component. Whether or not that is the case with Wikipedia I have no idea. $\endgroup$ – quicksort Jan 21 '17 at 11:55
  • $\begingroup$ Wikipedia sometimes has dead-end pages that contain no hyperlinks. If you get there, you are stuck. $\endgroup$ – Ran G. Jan 21 '17 at 17:33

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