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If we want a specific example, then how about the Erdos-Renyi random graph?

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    $\begingroup$ "Expander graphs" is not a class of random objects; they can be constructed deterministically. $\endgroup$
    – Jeffε
    Apr 4, 2013 at 9:01
  • $\begingroup$ Can you suggest a refinement of the question? What about Erdos-Renyi graphs? Is there a common random class of graphs known to be expanders for which this is not true with high probability? $\endgroup$
    – Elliot JJ
    Apr 4, 2013 at 23:58

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